Glossary
Symbols
(functional) excess risk, 26
0-1 loss, 13.1.2
Wiener-Kolmogorov filter
non-causal, 18.6.1
A
absence of arbitrage, 37a.1.3
absolute score, 7c.5, 7c.5
absolutely continuous component, 18.1.2
absolutely continuous spectral density, 18.1.2
abstract Bayes theorem, 7b.3.5
acceptance region, 30.1.1
accounting signals, 46c.1.4
accrued interest, 49.2.1
accuracy
binary classification, 13.4
action, 6.1.2
Bayes, 6.3.1
minimax, 6.4.1
action space, 6.1.2
activation function, 26.4.1
activity time, 38.8.2
actual cash-flow, 49.2.3
actual exchange rate, 49.2.3
actual value, 49.2.3
adapted basis, 31.1.3
adaptive execution algorithm, 47.3.2
additive, 7c.8.2
admissible, 22.8.1
affine quantile, 4b.4.3
affine transformation, 2b.3
algebraic multiplicity, 31.9.1
algebraic Riccati equation, 31.6.6
allocation policy, 43.6
almost everywhere
function equality, 34.3.1
alpha, 44.3.1
binary classification, 13.1
alternative beta, 46c
alternative hypothesis, 30.3
analysis of variance, 4a.5.2
ancestor, 15.1
angle, 31.3.3
anti-monotonic
function, 32.4.3
Arbitrage, 37a.17
arbitrage pricing theory, 37b.3.1
architecture, 26.4.1
area under curve (AUC), 13.1.4
arithmetic Brownian motion with drift, 21.1.2
Arrow-Debreu securities, 37b.1.2
Arrow-Pratt absolute risk aversion function, 44.5.1
ask size, 38.8.1
assets, 43.8.1
at the money, 38.4.2
foreign exchange market, 38.4.4
augmented view variables, 28.5.3
autocorrelation
function, 16.3
autocovariance function, 16.1.3
random field, spatial-fields
autoencoder, 14.1
autoregressive conditional duration, 20.5.2
autoregressive fractionally integrated moving average, 20.4
autoregressive moving average process
autoregressive
multivariate (VAR), ??
univariate (AR), ??
autoregressive polynomial, 17.3.1
companion matrix, 17.3.4
integrated
multivariate (VARIMA), relationships-varma-vma-var
univariate (ARIMA), ??
invertible, ??
LTI filter representation, 17.3.1
moving average
mutivariate (VMA), ??
univariate (MA), ??
moving average polynomial, 17.3.1
multivariate (VARMA), 17.3.1
univariate (ARMA), 17.3.1
Yule-Walker equation
univariate, ??
autoregressive of order one
univariate (AR), 17.2.1
vector (VAR), 17.2.1
auxiliary measure, 7c.6
B
Bachelier, 37d.2.1
backpropagation, 26.4.1, 33.2.3
backward cash-flow-adjusted value, 49.1.5
backward/forward exponential weighted moving average, 22.12.3
bagging, 22.11.1
balance sheet, 43.8.1
balanced, 22.9
bandpass filter, 18.2.4
bandwidth, 22.1.2
kernel density estimate, 22.3
bandwidth matrix, 22.1.2
base case, 28.6.1
base distribution, 28.1.1
base measure, 7c.6
basis, 31.1.2, 50.4.3
canonical, 31.1
orthonormal, 31.3.4
basis denominator, 50.4.3
basis instruments, 37b.1.1
Bayes classifier, 13.2.3
Bayes risk
of a decision, 6.3.3
of an action, 6.3.1
Bayes theorem, 4a.2.2
Bayesian networks, 15.6
benchmark, 50.5.1
Bernoulli distribution, 7c.5
best ask, 38.8.1
best bid, 38.8.1
best prediction, 31.3.5
beta
binary classification, 13.1
beta conditions
projection coefficients, 31.3.4
projection equation, 31.3.4
beta distortion index, 44.8.2
beta-adjusted excess return, 50.5.2
bets, 45b.4
between-cluster/group variance, 4a.5.2
Bhattacharyya coefficient, 22.11.4
bias, 25.1.1
binary classification, 13.1
bias reduction, 26
bid size, 38.8.1
bid-ask spread, 47.1
bilateral value adjustment, 43.3
binary classification, 13.1.5
binary classifier, 13.1.4
binary mixture distribution, 15.4
binary Gaussian mixtures, 15.4
binary mixture components, 15.4
binary normal mixtures, 15.4
binary partition encoder, 7c.5
binning, 38.8.3
binomial inverse theorem, 31.7.4
binomial tree, 20.1.2
bins, 7c.4.1, 38.8.3
Black-Merton-Scholes model, 37d.2.2
Bochner’s theorem, 34.6.1
bond yield, 42.3.2
bootstrap aggregating, 22.11.1
Borel sets, 7b.1.2
boundedness, 28.1.7
breadth, 26.4.1, 46a.4.4
breakdown point, 22.7.2
Brier scoring rule, 13.3.1
Brownian motion, 20.1.1
Buhlmann pricing equation, 37a.5
expectation, 37a.5
Buhlmann principle, 37c.2.4
butterfly, 37b.1.2, 38.4.4
C
calendar signal, 46c.1.4
calibrate, 37d
call option, 38.4.1
calm drivers, 43.7.3
canonical correlation matrix, 4b.4.3, 5b.3.1
canonical parameters, 7c.6
capital asset pricing model, 37b.2
capital gain, 49.1.6
cardinality, 34.1.2
cardinality constraint, 33.5, 35.2
carry signal, 46c.1.1
CART, 26.3.1
cash-flow function, 42.1
cash-flow-adjusted value, 49.1.5
categorical distributions, 7c.5
categories, 7c.5
Cauchy distribution, 7c.2.3
Cauchy transform, 2a.1.5
Cauchy-Schwarz inequality, 31.3.3
causal, 18.2.4
central tendency, 7a.2.1
affine equivariant, 7a.1.1, 7a.1.4
certainty-equivalent, 44.5
certainty-equivalent principle, 37c.2.2
chain rule
gradient, 32.1.2
matrix-variate, 32.1.3
multivariate, 32.1.2
univariate, 32.1.1
change of variable formula
multivariate, 32.3.4
univariate, 32.3.2
Chapman-Kolmogorov equations, 16.2.4
characteristic equation, 31.5.1
characteristic function
multivariate, 2a.1.4
univariate, 2a.1.4
characteristic matrix, 46c.5
characteristic polynomial, 31.5.1
characteristic portfolio, 46c.3
characteristic portfolios, 46c.5
Chebyshev’s inequality, 2b.4.2
chi-squared distribution, 7c.3.1
child, 15.1
child orders, 47
Cholesky decomposition, 31.6.5
Cholesky root
lower triangular, 31.6.5
upper triangular, 31.6.5
CIR, 21.2.2
claims, 38.6
classes, 7c.5
classical-equivalent, 22.8.1
classification
discriminative classification, 13.3.5
multinomial classification, 13.2
classification and regression trees, 26.3.1
clean price, 49.2.1, 49.2.1
clique, 15.1
maximal clique, 15.1
clique factorization, 15.7
clustering, 14.1.2
co-monotonic
function, 32.4.3
variables, 5a.2.4
co-monotonic additivity, 44.2
co-variogram
random field, 16.5.1
coalition, 35.2
codes, 14.1
coherent satisfaction measure, 44.9.1
coherent probability measure, 44.9.1
worst case expectation representation, 44.9.1
cointegrated, 16.3.4
cointegrated space, 39.2.1
cointegration signal, 46c.1.3
cointegration vector, 39.2.1
multivariate process, 16.3.4
collateral, 43.9.1
combination, 35.2
combinatorial heuristic, 35.2.6
2-step forward, 35.2.4
naive selection, 35.2.2
stepwise backward elimination, 35.2.4
stepwise bidirectional elimination, 35.2.4
stepwise forward selection, 35.2.3
combinatorial programming, 35.2
commonalities, 8.4.5
comparable instruments, 37d
complete, 37b.1.1
complete class theorem, 6.3.6
complete metric space, 34.3.1
compound distribution, 4a.2.3
compound Poisson process, 21.1.3
compounded rate of return
(instantaneous) compounded rate of return, 50.4.6
average compounded rate of return, 50.4.6
compounded return, 50.4.1
Comprehensive Capital Analysis and Review, 43.7
concave down function
univariate, 32.5.1
concave function
multivariate, 32.5.2
univariate, 32.5.1
concave up function
univariate, 32.5.1
concavity, 44.2
condition number, 23.6.2
conditional cdf, 4a.2.1
conditional covariance, 4a.5.2
conditional excess distribution, 44.6.2
conditional expectation, 4a.5.2
Stochastic processes, 16.1.5
with respect to partition, 7b.3.3
conditional independence, 4a.3, 22.9
conditional mode, 4a.5.1, 4a.5.3
conditional pdf, 4a.2.1
conditional pmf, 4a.2.1
conditional principal component analysis, 8.6.16
conditional principal directions, 8.6.16
conditional principal variances, 8.6.16
conditional probability, 7b.1.6
with respect to partition, 7b.3.2
conditional quantile, 4a.5.3
conditional value at risk, 44.8.2
conditioning-marginalization, 28.1.3
cone, 33.3.6
confidence, 30.1.1
confusion matrix, 13.1
conic programming, 33.3.6
conjugate distribution, 22.8.3
consistency with weak dominance, 44.2
consistent with q-th order dominance, 44.2
constancy, 44.2
constant proportion portfolio insurance, 46d.4.1
constraint set, 33.1.1
selection, 33.5
contingency table, 13.2.1
continuous-state distributions, 20.1
control variable, 11.1.3
convex function
multivariate, 32.5.2
univariate, 32.5.1
convex programming, 33.3
epigraph form, 33.6.2
convex set, 32.5.2
convexity, 42.3.2, 42.3.2
effective key-rates, 42.3.2
risky investment, 46d.6
satisfaction/risk measures, 44.2
convolution, 34.4.3
cyclic, 34.4.7
discrete, 34.4.5
integral, 34.4.4
periodic, 34.4.6
convolution theorem, 34.4.3
coordinate descent, 33.5.4
copula, 5a.2.2, 5a.2.2
copula-marginal combination, 5a.4.2
copula-marginal distributions, 5a.4.2
copula-marginal separation, 5a.4.1
copula-pdf, 5a.2.3
Cornish-Fisher approximation, 44.6.2
Cornish-Fisher expansion, 44.6.2
correlation, 5b.3
correlation function, 5b.3
correlation matrix, 5b.3
cost of equity, 37d.1.1
cost of trading, 46d.6
counterparty credit risk, 43.3
coupling function
non-linear, 4a.4.3
coupon, 38.10.2
coupon bond, 38.3.1
CoVaR, 43.7.1
covariance
abstract, 7b.2.1
covariance inner product, 7b.2.6
covariance matrix, 2b.1.2
cross-covariance, 2b.1.2
partial, 4b.2
covariance principle, 37a.5
covariant, 3.1.1
covariates, 11.1
Cramer decomposition, 18.1.2
Cramer-Lundberg ruin model, 43.8.5
credit ratings, 38.5.3
credit structural model, 38.5.2
credit value adjustment , 43.3
critical point, 33.2.1
critical region, 30.1.1
cross the spread, 47.1
cross-autocorrelation
function, 16.1.3
cross-autocovariance
function, 16.1.3, 16.3
cross-entropy, 11.4.1
cross-sectional, 46c, 46c
cross-sectional linear factor model, 8.5
cross-sectional sample median of default probabilities, 38.5.3
cross-spectral density, 18.1.2
cumulant , 41.7.1
cumulative cash-flow, 49.1.3
cumulative distribution function
multivariate, 2a.1.1
univariate, 2a.1.1
cumulative link, 7c.5.2
cumulative monetary amount, 38.8.1
cumulative number of migrations, 38.5.3
cumulative P&L, 38.9
cumulative signed volume, 38.8.1
cumulative trade sign, 38.8.1
cumulative volume, 38.8.1
currency carry trade, 42.2.2
curvature, 38.3.5
curve, 31.4.4
curve/surface signals, 46c.1.4
cutoff classifier, 13.1.4
D
data, 22.4.1
data-generating process, 6.1.1
debt, 43.8.1
debt value adjustment, 43.3
decay, 38.3.5
decision
deterministic, 6.3
decision function
admissible, 6.3.6
Bayes, 6.3.3
minimax, 6.4.1
optimal posterior, 6.3.4
randomized, 6.3
decision problem
statistical, 6.1
decision region
binary classification, 13.2.3
decision regions
multinomial classification, 13.2
decoder, 14.1
decomposition
linear, weak, 4b.4.4
non-linear, strong, 4a.4.3
decreasing function, 32.4.1
entrywise, 32.4.2
matrix-valued, 32.4.2
strictly, 32.4.1
degree of reversal, 46c.3.3
delta, 38.4.4
delta p, 13.4
delta rule, 26.4.1
dependent variables, 8.1, 11.1
depth, 26.4.1
derivative
directional, 32.1.2
first, 32.1.1
higher order, 32.1.1
partial, 32.1.2
second, 32.1.1
total, 32.1.2
univariate, 32.1.1
descendant, 15.1
design of experiments, 11.1.3
determinant, 31.2.3
deviation
expectile, 7a.2.3
maximum, 7a.2.4
mean absolute, 2a.4.3
median absolute, 2a.4.3
subquantile, 7a.2.3
differentiable function
multivariate, 32.1.2
univariate, 32.1.1
Differential entropy, 11.4.1
dimension, 31.1.2
Dirac delta, 34.3.2
direct sum, 31.1.3
directed graph, 15.1
dirty price, 49.2.1
discount, 38.10.2
discount factor, 49.2.3
discount function, 42.1
discounted cash-flow, 37d.1.1
discounted cash-flow adjusted value, 37c.3.1
discounted payoff, 37c.2
discrete derivative
central first order, 35.1.1
central second order, 35.1.1, 35.1.2
discrete distribution, 2a.1.3
discrete Laplacian, 35.1.2
discrete-state distributions, 20.1
discrete-state random walk, 20.1.2
discriminant variables, 7c.5
discriminative model, 11.2.2
generative embedding, 11.2.2
discriminative next-step model, 39.1.6
dispersion, 7a.2.1
affine equivariant, 7a.1.1
distance, 31.4.2
absolute, 31.4.2
Euclidean, 31.3.3
identity of indiscernibles, 31.4.2
Lp, 34.3.5
Mahalanobis, 31.4.2
p, 31.4.2
subadditivity, 31.4.2
symmetry, 31.4.2
triangle inequality, 31.4.2
distance matrix, 13.2.1
distance to default, 20.3.4
distorted cdf
satisfaction indices/risk measures, 44.8.1
distorted pdf
satisfaction indices/risk measures, 44.8.1
distortion function, 44.8.1
distortion principle, 37c.2.3
distortion satisfaction measure, 44.8.1
distribution
(absolutely) continuous, 2a.1.2
mixed, 2a.1.1
distributional view, 28.1.3
divergence, 31.4.3
Bregman, 31.4.3
difference, 31.4.3
extended f, 31.4.3
identity of indiscernibles, 31.4.3
separable, 31.4.3
diversification distribution, 45b.4
diversity, 22.11.4
dividend-adjusted value, 38.1
stocks, 49.1.5
divisors, 7c.8.3
dollar duration, 43.2.1
dollar-neutral constraint, 46c.3.2
domain
circle, 34.1.1
continuous, 34.1.1
cyclic group, 34.1.1
discrete, 34.1.1
frequency, 34.4
space, 34.4
time, 34.4
torus, 34.1.1
dominant-residual LFM, 8.1.2
dot product, 31.3
drawdown, 50.6
maximum (absolute) drawdown, 50.6
maximum percentage drawdown, 50.6
percentage drawdown, 50.6
dual Legendre, 3.1.3
dually flat, 3.1.3
duration, 42.3.2
effective key rates, 42.3.2
DV01, 43.2.1
dynamic allocation, 46c
dynamic conditional correlation, 40.1.3
dynamic linear factor model, 18.6
dynamic principal component, 18.6.2
dynamic regression linear factor model, 18.6.1
E
e-affine coordinates, 3.1.2
e-flat, 3.1.2
e-geodesic, 3.1.2
EBITDA, 43.8.2
economic capital, 44.12
economic net income, 43.8.2
edges, 15.1
effective delta, 42.3.3
effective duration
effective, 42.3.2
effective number of bets, 45b.4
effective number of scenarios, 22.1.4
effective rank, 28.1.6
effective rho, 42.3.3
key-rates, 42.3.3
effective volga, 42.3.3
efficient frontier, 46a.1
efficient market hypothesis, 20.1
eigenfunction
kernel, 34.2.4
operator, 34.2.4
eigenvalue
linear transformation, 31.5.1
matrix, 31.5.1
operator, 34.2.4
eigenvector
linear transformation, 31.5.1
matrix, 31.5.1
elastic net, 22.10.2, 33.4.3
constrained generalized elastic net, 33.5.4
elicitability
satisfaction measures, 44.2
elicitable, 2a.4.1
ellipsoid, 2b.2.2
location-dispersion, 7a.1.4
mean-covariance, 2b.2.2
ellipsoid test for invariance, 19.1
elliptical distribution, 7c.2.1
EM algorithm
population, 29.2.6
empirical histogram, 7c.4.1
normalized, 7c.4.1
encoder, 14.1
enterprise value, 37d.1.2
entropy
generalized , 6.3.1
equally weighted portfolio, 46a.1.3
equilibrium performance model
Black-Litterman, 27.8
equilibrium returns, 46a.1.3
equity, 43.8.1
equity book value, 43.8.1
equivalent optimization problem, 33.6
ergodic
in autocovariance, 16.3.2
in mean, 16.3.2
strong, 16.3.2
Erlang process, 21.1.3
error
mean-squared, var-sol-loc-disp
multivariate mean absolute, 7a.2.7
univariate, 7a.2.1
error prediction matrix
linear, 4b.2
Esscher principle, 37c.2.4
estimable, 44.2
estimate, 25.1
estimation, 11.3
estimation model, 23.5
Bayesian estimation, 22.8.1
estimation set, 22.9
point prediction, 25.3.1
predictive distribution, 25.4.1
estimation uncertainty, 22.8.1
estimator, 25.1
European-style derivatives, 38.4
evidence
maximum likelihood, 22.4.1
evidence lower bound, 29.2.5
ex-dividend date, 49.1.2
exotic beta, 46c
expectation
abstract, 7b.1.3
expectation angle, 7b.2.2
expectation distance, 7b.2.2
expectation function, 16.1.3
random field, 16.5.1
expectation inner product
multivariate, 7b.2.4
univariate, 7b.2.1
expectation length, 7b.2.2
expectation parameters, 7c.6
expectation rule, 7c.4.3
expectation-maximization, 22.5.2
expectation step, 22.5.2
maximization step step, 22.5.2
expected drawdown, 44.3.1
expected overperformance, 44.3.1
expected shortfall, 44.8.2
expected utility, 44.5
expected value of the process variance (EVPV), 4a.5.2
expectile, 2a.4.3
expectile-VaR, 44.9.2
expiry, 38.4
explanatory variables, 11.1
exponential decay probabilities, 22.1.1
exponential family distribution, 7c.6
exponential kernel, 22.1.2
exponential of the entropy, 22.1.4
exponential operator, 32.2.1
exponential principle, 37c.2.2
exponential tilting, 28.1.5
exponentially weighted moving average, 22.2.4
exponentially weighted moving correlation, 22.2.4
exponentially weighted moving covariance, 22.2.4
exponentially weighted moving quantile, 22.2.4
exponentially weighted moving standard deviation, 22.2.4
exposure, 43.2.1
portfolio P&L, 46c.3
risky investment, 46d.6
exposure at default, 38.5.2
extrema
local, 33.1.2
relative, 33.1.2
extreme value theory, 44.6.2
F
f-divergence, 3.1.4
F-measure
binary classification, 13.4
F1 score
binary classification, 13.4
face value, 38.3.1
factor analysis, 23.6.6
confirmatory, 8.4
equamax, 8.4.4
exploratory, 8.4
orthomax, 8.4.4
parsimax, 8.4.4
quartimax, 8.4.4
varimax , 8.4.4
factor analysis matrix, 23.6.6
factor loadings, 8.1
factor premia, 46c.5.2
factor premium, 46c.2
factor-analysis linear factor model, 8.4.1
factor-replicating portfolios
arbitrage pricing theory, 37b.3.1
factors, 11.1, 46c
linear factor model, 8.1
fair value, 49.1.2
fallout, 13.1
false negative
accuracy, 13.1
probability, 13.1
rate, 13.1
false positive
accuracy, 13.1
probability, 13.1
rate, 13.1
feature engineering, 12.1
feature map
canonical, 34.7.2
Mercer, 34.7.2
Feller condition, 21.5.1
filter, 18.2
anti-causal operator, 18.2
causal operator, 18.2
factor construction, 18.6.2
invertible, 18.2
linear time invariant , 18.2.4
filtering, 11.3
filtration, 16.6.1
adapted process, 16.6.3
(fully-recombining) binomial tree, 16.6.3
(fully-recombining) tree, 16.6.3
martingale, 16.6.4
Radon-Nikodym process
martingale, finite-discrete-time-stoch-process-sec
set
natural, 16.1.5
financial instrument, 49.1.1
finite difference
backward first order, 35.1.1
central first order, 35.1.1, 35.1.2
central second order, 35.1.2
forward first order, 35.1.1
finite-dimensional joint distributions, 16.1.2
first in, 45b.1.1
first order criterion, 33.2.1
first order differential, 32.1.2
matrix-variate, 32.1.3
Fisher consistent, 22.7.1
Fisher discriminant analysis (FDA), 13.1.8
Fisher information distance, 3.1.4
Fisher’s linear discriminant, 13.1.8
flexible probabilities, 40
estimation, 7c.4
forecast, 8.1
mean-covariance, 11.2
point, 11.2
probabilistic, 11.2
forecasting
inference, 11.3
foreign exchange function, 42.1
foreign exchange rate, 38.2.1
forward, 38.2.2
forward cash-flow-adjusted value, 49.1.5
forward exchange rate, 38.2.1
forward rate, 38.10.2
forward swap, 38.3.1
forward variance swap rate, 38.4.6
Fourier transform, 34.4.3
discrete (DFT), 34.4.7
discrete time (DTFT), 34.4.5
Fourier series, 34.4.6
integral, 34.4.4
inverse, 34.4.3
fractional Brownian motion, 21.4
Frechet derivative, 34.8.2
second order, 34.8.3
Frechet-Hoeffding bounds, 5b.1.1
full-investment, 46c.3.2
fully constrained LFM, 8.6.17
function space, 34.2.1
addition, 34.2.1
scalar multiplication, 34.2.1
functional, 34.8
functional derivative, 26.5
fundamental accounting equation, 43.8.1
fundamental law of active management, 46a.4.4
fundamental linear factor model, 8.5
fundamental signals, 46c.1.4
fundamental theorem of asset pricing, 37a.2.2
martingale pricing formula, 37b.4.3
fundamental theorem of calculus
first, 32.3.3
second, 32.3.3
funding risk, 43.3
funding value adjustment, 43.3
G
gamma distribution, 7c.3.2
Gateaux derivative, 34.8.1
Gaussian kernel, 22.1.2, 22.3
generalized autoregressive conditional heteroscedastic, 20.5.1
generalized excess return, 50.5.2
generalized linear models (GLM), 12.3.6
generalized linear return, 50.4.3
generalized method of moments
iterated GMM, 23.6.5
generalized method of moments with flexible probabilities (GMMFP) estimate, 22.6.3
minimization, 22.6.4
generalized negative entropy, 11.4.1
generalized Pareto distribution, 44.6.2
generalized spectral density, 18.1.2
generalized weight, 50.4.4
generative model, 11.2.2
generative next-step model, 39.1.6
generator
Markov chain, 21.3.1
matrix, 31.2.3
generic position, 43.1.3
geodesic
metric, 31.4.4
geodesic space, 31.4.4
geometric Brownian motion, 42.1.1
geometric multiplicity, 31.9.1
Gibbs distribution, 15.7
Gini coefficient, 13.1.4
Giny impurity, 13.3.3
glasso, 23.6.5
Tikhonov, 22.10.3
Glivenko-Cantelli theorem, 22.2.1
Gordon growth model, 37d.1.1
grade, 5a.1
grades, 5a.2.1
gradient, 32.1.2
matrix-variate, 32.1.3
vector-valued function, 32.1.2
gradient descent, 33.2.3
stochastic, 33.2.3
Gram matrix, 31.6.1
Gram-Schmidt process
backward, 31.6.5
forward, 31.6.5
Gramian, 31.6.1
grand mean, 23.6.1
graph, 15.1
directed acyclic, 15.1
graphical lasso, 23.6.5
Greeks, 42.3
gross exposure, 43.2.1
group
general linear, 31.2.3
orthogonal, 31.3.6
special orthogonal, 31.3.6
unitary, 31.3.6
growth stocks, 46c.1.2
H
Hadamard product, 31.7.2
half-life, 17.2.2, 22.1.1
Hamiltonians, 7c.6
harmonic process
multivariate, ??
univariate, 17.6
hat matrix, 4b.2
hazard function, 2a.1.5
Hellinger distance, 22.11.4
Herglotz theorem, 34.6.1
Hessian, 32.1.2
matrix-variate, 32.1.3, 32.1.3
Heston model, 37d.2.3
hidden Markov model, 20.6
hidden variables, 11.1
maximum likelihood, 22.5
point prediction, 25.3.1
high breakdown estimators, 22.7.2
high breakdown point with flexible probabilities, 22.7.2
high minus low, 46c.2
high water mark, 50.6
Hilbert space, 34.3.1
historical cdf, 22.2.1
historical cross-sectional, 8.5.7
historical distribution, 22.2.1
historical pdf, 22.2.1
historical principal component, 8.3.7
historical repricing, 42.5.2
historical with flexible probabilities (HFP) autoencoder, 25.3.4
historical with flexible probabilities (HFP) cdf, 22.2.2
historical with flexible probabilities (HFP) correlation matrix, 23.1
historical with flexible probabilities (HFP) covariance matrix, 23.1
historical with flexible probabilities (HFP) distribution, 22.2.2
historical with flexible probabilities (HFP) estimate, 22.2.3
historical with flexible probabilities (HFP) mean, 23.1
historical with flexible probabilities (HFP) median, 22.7.2
historical with flexible probabilities (HFP) pdf, 22.2.2
historical with flexible probabilities (HFP) predictor, 25.3.4
historical with flexible probabilities (HFP) quantile, 22.7.2
historical with flexible probabilities (HFP) standard deviation vector, 23.1
hold-out, 25.3.5
Hotelling statistic, 30.3.2
Hurst coefficient, 21.4
hybrid Monte Carlo-historical, 41.5.2
I
ice-cream cone, 33.3.4
identity transformation, 31.2.3
idiosyncratic, 8.1.3
ill-conditioned, 23.6.2, 33.4
ill-posed, 33.4
IM algorithm, 29.2.5
image space, 31.2
implementation shortfall, 50.3
implied returns, 46a.1.3
implied volatility, 38.4.3
implied volatility surface, 38.4.3
improper integral, 32.3.2
impulse response, 18.2.4
in the money, 38.4.2
in-sample error, 22.230
inception, 50.2.2
income, 49.1.6
income statement, 43.8.2
increasing function, 32.4.1
entrywise, 32.4.2
matrix-valued, 32.4.2
strictly, 32.4.1
indefinite integral, 32.3.3
independence
events, 4a.1
random variables, 4a.1
independent component analysis, 4a.4.2
independent variables, 11.1
linear factor model, 8.1
induced expectation, 44.10.1
inefficiency, 25.1.1
inference, 11.3
marginalization, 11.3
marginalization problem, 11.3
infinitely divisible, 7c.8.3
inflator, 37a.2.2
influence function, 22.7.1
information, 16.1.5
generator, 16.1.5
linearized, 16.1.5
random time series, 40
set, 16.1.5
set, of a random variable, 7b.1.2
information coefficient, 46a.4.1
information measure, 11.4.1
information ratio, 44.11.1
linearly predicted, 46a.4.1
information set
distributions, 29.2.1
linearized, 4b.2.1
information/view, 28.6.1
informedness, 13.4
inner product, 31.3
Hermitian, 34.3.1
Hermitian symmetry, 34.3.1
L2, 34.3.1
linearity, 31.3
partial linearity, 34.3.1
positive definiteness, 31.3, 34.3.1
statistical , 2b.2.3
symmetry, 31.3
inner product space, basic-geom-sec
innovation
linear, weak, 4b.4.4
linear, weak, standardized, 4b.4.4
non-linear, strong, 4a.4.3
weak, 4b.2
Innovation process
Mean-covariance, 16.4.1
Error decomposition matrix, 16.4.1
Probabilistic uncorrelated, 16.4.1
Error decomposition matrix, linear-weak-decomp-secc
input variables, 6.3
inputs, 11.1
instantaneous exchange rate, 49.2.3
instantaneous forward curve, 38.10.2
instantaneous forward rate, 38.10.2
instantaneous spot rate, 38.10.2
integral kernel, 34.2.3
Mercer, 34.5.2
positive definite, 34.5.2
symmetric, 34.5.2
integral power spectrum
matrix-valued, 34.6.3
integrated
fractionally, 16.3.3
order d, 16.3.3
order zero, 16.3.1
integration by parts, 32.3.2
integration operator, 6.2.2
intensity, 21.1.3
intensity models, 37d.3.2
interaction, 26.2.1
interest rate, 38.3.3
internal rate of return, 50.4.6
interquantile range, 7a.1.3
intuitive r-squared, 8.5.5
invariance rule, 7c.4.3
invariant, 7a.1.4
Invariant process
Mean-covariance, 16.4.1
probabilistic, 16.4.1
Probabilistic uncorrelated, 16.4.1
Standardized mean-covariance, 16.4.1
standardized probabilistic, 16.4.1
Standardized probabilistic uncorrelated, 16.4.1
invariants, 39
inverse, 31.2.3
inverse transform sampling, 5a.1
inverse-call, 38.3.4
inverse-Wishart distribution, 7c.3.4
invertible, 31.2.3
investment factor, 50.4.6
reinvested instrument, 49.1.4
iso-contour, 2a.2
isolated, 45b.1.1
iterated integral, 32.3.4
J
jackknife estimator, 22.7.1
Jacobian, 32.1.2
James-Stein estimator, 23.6.1
Jeffreys prior, 22.8.1
joint scenario, 7c.4
jump component, 18.1.2
jump rule, 49.1.3
jump spectral density, 18.1.2
K
k-fold, 25.3.5
k-means clustering, 14.1.2
kalman filter, 17.5.6
kalman gain matrix, 17.5.6
kappa ratio, 44.11.2
Karush-Kuhn-Tucker conditions, 33.2.2
Kendall’s tau, 5b.2.1
kernel, 22.3
of a linear transformation, 31.2
kernel density estimate, 22.3
kernel principal component analysis, 14.1.3
kernel stochastic discount factor, 37a.2.3
kernel trick, 26.6, 34.7.2
linear kernel, 26.6
polynomial kernel, 26.6
radial basis functions, 26.6
kernel with flexible probabilities (KFP) generalized mean, 22.3
kernel with flexible probabilities (KFP) pdf, 22.3
key rates, 38.3.5
Kolmogorov-Smirnov test, 19.1
Kronecker delta, 34.3.2
Kronecker product, 31.7.2
Kullback-Leibler divergence, 3.1.4, 11.4.1
L
L2 space, 7b.2.1, 34.3.1
Lévy process, 16.2.2
label encoding, 32.3.1
labels, 11.1
lag operator, 18.2, 32.2.1
Lagrange multiplier, 33.2.2
Lagrangian function, 33.2.2
Laplace approximation, 7a.1.4
Laplacian, 32.1.2
large capitalization stocks, 46c.1.4
lasso, 22.10.2, 33.5.4
lasso regression, 24.4.2
lasso shooting, 33.5.4
last in, 45b.1.2
last transaction price, 38.8.1
latent variables, 11.1
maximum likelihood, 22.5
law invariant, 44.2
law of iterated expectations, 4a.5.2
law of one price, 37a.1.1
law of the unconscious statistician, 2a.3.3
law of total covariance, 4a.5.2
law of total linear covariance, 8.6.13
law of total linear variance, 8.6.13
law of total variance, 4a.5.2
LDL-Cholesky decomposition, 31.6.5
leaf, 26.3.1
learning, 11.3
least favorable prior, 6.3.5
least-squares residual, 12.1.2, 12.1.2
leave-1-out, 25.3.5
leave-p-out, 25.3.5
Lebesgue’s decompositon theorem, 34.1.3
left singular vector, 31.5.4
Legendre transformation, 3.1.3
length, 31.4.1, 31.4.4
Lp, 34.3.5
level, 38.3.5
leverage, 43.2.2
leverage effect, 20.5.2
Levy process, 21.1.1
Levy-Khintchine, 21.1.5
liabilities, 43.8.1
Libor, 38.10.2
likelihood, 23.5
estimators as random variables, 25.1.1
maximum likelihood, 22.4.1
likelihood ratio, 13.1.3
likelihood-ratio test, ??
limit order book, 38.8.1
limit order placement, 47.3
linear classification, 13.80
bias, 13.1.5
linear combination, 31.1.2
linear coupling, 4b.4.3
linear dependence, 31.1.2
linear discriminant analysis (LDA), 13.3.6
linear factor model, 8.1
linear independence, 31.1.2
linear innovation
non-standardized, 4b.4.3
linear law of iterated projections, 8.6.13
linear loss matrix, 4b.2
linear operator
“flat”, 31.3
linear pricing equation, 37a.2.1
intertemporal, 37b.4.2
linear programming, 33.3.2
linear quantile matrix, 4b.4.1
linear regression, 4b.2
linear return, 50.4.1
linear space, 31.1.1
linear state space model, 17.5.1
observation equation, 17.5.1
transition equation, 17.5.1
linear state-space model
covariance stationary, 17.5.2
systematic-idiosyncratic, 17.5.4
linear time invariant filter
frequency response function, 18.2.4
transfer function, 18.2.4
linear transformation, 31.2
symmetric, 31.3.1
linearity, 37a.1.2
linearly constrained quadratic programming, 33.3.3
link function, 7c.6
links, 15.1
liquidation, 50.2.2
liquidation valuation, 43.1.5
liquidity curve, 47.1
"market buy" liquidity curve, 47.1
"market sell" liquidity curve, 47.1
local Markov property, 15.6
location, 7a.2.1
affine equivariant, 7a.1.1, 7a.1.4
log-partition function
exponential family distribution, 7c.6
log-return, 50.4.6
log-sum-exp function, 7c.6.2
logistic function, 7c.380
logistic regression
binary, 13.3.6
multinomial, 13.3.6
logit function, 7c.6.2
logit parametrization
binary logit parametrization, 7c.5.2
multinomial logit parametrization, 7c.5.2
logit regression
binary, 13.3.6
multinomial, 13.3.6
lognormal distribution, 7c.9.1
shifted, 7c.9.1
long holdings, 50.1
long memory, 20.4
long position, 43.1.1
longitudinal data, 22.9
Lorentz cone, 33.3.4
Lorenz curve, 2a.1.5
loss, 13.1.5
0-1 loss, 13.1.5
0-1 margin loss, 13.1.5
consistent, 2a.4.1
Dawid-Sebastiani, 2b.4
exponential , 13.1.5
hinge , 13.1.5
logistic , 13.1.5
margin loss, 13.1.5
probabilistic worst-case, 6.4.1
proper, 6.5.4
square , 13.1.5
strictly proper, 6.5.4
tangent , 13.1.5
worst-case, 6.4.1
loss function, 6.1.3
loss given default, 38.5.2
lower partial moment, 44.9.2
root, 44.9.2
lower partial moment principle, 37c.2.1
Lp space, 34.3.5
M
m-affine coordinates, 3.1.2
m-flat, 3.1.2
m-geodesic, 3.1.2
m-square, 42.3.2
machine learning
experimental study, 11.1.3
interventional study, 11.1.3
observational study, 11.1.3
macro signals, 46c.1.4
macroeconomic linear factor model, 8.2
Mahalanobis inner product, 31.3.2
Marchenko-Pastur distribution, 23.6.3
marginal cdf, 2a.3.1
marginal characteristic function, 2a.3.1
marginal contributions, 45b
Euler decomposition, 45b.2
Euler marginal contributions, 45b.2
marginal distribution, 2a.3.1
marginal pdf, 2a.3.1
marginal pmf, 2a.3.1
marginal supply demand curve, 47.1
marginalization
mean-covariance, 2b.3.4
probabilistic, 2a.3.1
marked-to-market, 49.1.2
marked-to-model, 49.1.2
markedness, 13.4
market beta, 46c.3
market capitalization, 43.8.1
market impact, 47.1.3
market impact decay kernel, 47.1.3
market impact function, 47.1.3
market impact model, 47.1.3
market impact P&L, 47.2.2
market impact square root law, 46a.3.3
market order placement, 47.3
market parameters, 37d
market portfolio, 46c.2
Markov chain
Monte Carlo, 29.1
Markov network, 15.7
Markov process, 16.2.4
mean-covariance, 16.2.4
time homogenous, 16.2.4
Markov’s inequality, 2b.4.2
MARS, 26.3.1
martingale, 16.2.3
matrix, 31.2.1
addition, 31.2.2
anti-symmetric, 31.5.3
circulant, 34.4.2
commutation, 31.7.4
conformable, 31.2.2
conjugate transpose, 31.3.1
decomposition, 31.7.4
Hermitian, 31.3.1
identity, 31.2.3
inverse, 31.2.3
invertible, 31.2.3
low-rank-diagonal, 31.7.4
multiplication, 31.2.2
negative definite, 31.3.2
negative semidefinite, 31.3.2
non-singular, 31.2.3
orthogonal, 31.3.6
polynomial, 31.8
positive definite, 31.3.2
positive semidefinite, 31.3.2
rank property, 31.7.4
scalar multiplication, 31.2.2
size, 31.2.1
square, 31.2.1
subtraction, 31.2.2
symmetric, 31.3.1
Toeplitz, 34.4.1
transpose, 31.3.1
transpose-square-root, 31.6.3
unitary, 31.3.6
matrix exponential, 31.7.2
matrix-normal distribution, 7c.1.6
matrix-valued kernel, 34.5.3
Mercer, 34.5.3
positive definite, 34.5.3
symmetric, 34.5.3
matrix-vector multiplication, 31.2.1
Matthews correlation, 13.4
maturity, 38.3.1
maximal Youden’s J statistic, 13.1.4
maximum
global, 33.1.1
local, 33.1.2
relative, 33.1.2
maximum a posteriori, 4a.2.2
maximum classifier, 13.1.4
maximum expected return portfolio, 46a.1.1
maximum information ratio portfolio, 46a.1.1
maximum likelihood factorization, 15.3.2
maximum likelihood parameters, 22.4.1
maximum likelihood with flexible probabilities, 22.4.3
normal assumption, 24.2.2
Student t assumption, 24.2.3
maximum likelihood with flexible probabilities (MLFP) estimate, 22.4.4
maximum likelihood with flexible probabilities (MLFP) predictor, 25.3.4
maximum partition encoder, 7c.5
maximum return signal-to-noise portfolio, 46a.1.1
maximum Sharpe ratio portfolio, 46a.1.1
mean maximum information ratio, 46a.4.1
mean reversion, 20.2
mean vector, 2b.1.1
mean-covariance equivalence class, 2b.1.3
mean-lower partial moment, 44.9.2
mean-semideviation, 44.9.2
measure, 34.1.2
absolutely continuous, 34.1.3
counting, 34.1.2
finite, 34.1.2
integral, 34.1.2
Lebesgue, 34.1.2
Radon-Nikodym derivative, 34.1.3
Riemann-Stieltjes, 34.1.2
measure of concordance, 5b.2
measure of dependence, 5b.1
median, 2a.4.3
multivariate, 7a.2.7
Mercer’s theorem, 34.7.1
method of moments (MM) estimate, 22.6.1
method of moments with flexible probabilities (MMFP) estimate, 22.6.1
metric, 31.4.2
discrete, 31.4.2
metric geodesic, 3.1.2
metric space, 31.4.2
Metropolis-Hastings algorithm, 29.1.1
microprice, 38.8.1
mid-quote, 38.8.1
midrange, 7a.2.4
minimum
global, 33.1.1
local, 33.1.2
relative, 33.1.2
minimum relative entropy numeraire probability, 37a.2.3
minimum relative entropy principle, 28.1.4
minimum relative entropy stochastic discount factor, 37a.2.3
minimum tracking error portfolio, 46a.1.1
minimum variance portfolio, 46a.1.1
minimum-torsion bets, 45b.4.1
minimum-torsion exposures, 45b.4.1
minimum-torsion transformation, 45b.4.1
misclassification error, 7a.2.4
Misclassification scoring rule, 13.3.1
miss rate, 13.1
mixture models, 15.4
Gaussian mixtures, 15.4
mixture of experts, 12.4.2
modal dispersion, 7a.1.2
modal square-dispersion, 7a.1.4
mode
multivariate, 2a.4
univariate, 2a.4
model
frequentist approach, 25.4.2
frequentist prediction, 25.3.2
model set
distributions, 29.2.1
model uncertainty, 6.3.7
moment generating function
multivariate, 2a.1.5
momentum, 46c.1.3
momentum signal, 46c.1.3
money multiple, 50.4.6
money-equivalence, 44.2
moneyness, 38.4.2
monotone map
decreasing, 32.4.3
increasing, 32.4.3, 32.4.3
strictly increasing, 32.4.3
monotonic function, 32.4.1
entrywise, 32.4.2
matrix-valued, 32.4.2
strictly, 32.4.1
monotonicity, 28.1.7, 44.2
mortgage backed securities, 49.2.1
most powerful set, 13.1.3
multinomial logit function, 7c.6.2
multinomial mixture distribution, 15.4
multinomial Gaussian mixtures, 15.4
multinomial mixture components, 15.4
multinomial normal mixtures, 15.4
multinomial probit regression, 13.3.8
multiple, 49.1.4
multiple of invested capital (MOIC), 50.4.5
multivariate adaptive regression splines, 26.3.1
multivariate arithmetic Brownian motion, 46d.1.1
multivariate Gaussian, 22.1.2
multivariate generalized autoregressive conditional heteroscedastic, 39.1.5
multivariate geometric Brownian motion, 46d.1.1
multivariate Ornstein-Uhlenbeck, 21.6
musical isomorphism, 31.3
N
naive Bayes models, 15.5
natural form, 7c.6
natural parameters, 7c.6
neighbors, 15.1
nested simulation, 42.5.2
net asset value, 43.1.4
net exposure, 43.2.1
neural network
artificial, 26.4.1
convolutional, learning-deep
deep artificial, 26.4.1
neuron, 26.4.1
convolution, 26.4.1
neutralization, 46c.1.5
Newton’s method, 33.2.4
Neyman-Pearson lemma, 13.1.3
nodes, 15.1
non-linear error prediction matrix, 4a.5.2
non-linear partial covariance matrix, 4a.5.2
norm, 31.4.1
absolute homogeneity, 31.4.1
counter, 31.4.1
Frobenius, 31.4.1
Lp, 34.3.5
Mahalanobis, 31.3.3
matrix p, 31.4.1
maximum, 31.4.1
p, 31.4.1
positive definiteness, sec-norms
standard Euclidean, 31.3.3
subadditivity, 31.4.1
taxicab, 31.4.1
norm symmetric, 5a.3.2
normal copula, 5a.3.1
normal distribution, 7c.1
normal-inverse-Wishart (NIW) distribution, 23.5.2
normalized value characteristics, 46c.3
normalizing and variance stabilizing, 20.5.3
normed vector space, 31.4.1
notional value, 38.3.1
nowcasting
inference, 11.1
null hypothesis, 30.3
null space, 31.2
nullity
linear transformation, 31.2
number of obligors, 38.5.3
numeraire, 37a.2.2
risk-free , 37a.3.1
risk-neutral, 37a.3.1
numeraire probability measure, 37a.2.2
O
objective function, 33.1.1
observable features, 37d
observable variables, 11.1
offset cash, 50.4.4
omega ratio, 44.11.2
one-hot encoding
partitions, 32.3.1
one-versus-one (OvO) classifier, 13.2.6
one-versus-the-rest classifier, 13.2.6
operational loss, 38.7
operations, 38.7
operator, 34.2.2
differentiation, 34.2.2
integral, 34.2.2
invertible, 34.2.2
linear, 34.2.2
unitary, 34.3.4
opportunity cost, 6.1.3
optimal discriminants, 13.2.3
optimal relative scoring, 13.1.3
optimal score, 13.1.3
optimal scoring, 13.1.3
optimization
problem, 33.1.1
unconstrained, 33.1.1
option-based portfolio insurance, 46d.3
order placement, 47
order routing, 47
order scheduling, 47
ordered logit, 7c.5.2
ordered probit, 7c.5.2
ordinal classifier, 13.1.4
ordinal partition encoder, 7c.5
ordinary least squares, 8.2.6
ordinary least squares with flexible probabilities, 8.2.6
Ornstein-Uhlenbeck, 21.2.1
orthogonal, 31.3.3
projection, 31.3.4
projection equation, 31.3.4
to a linear subspace, 31.3.4
transformations, 31.3.6
orthogonal-increment process, 16.2.3
orthogonality in expectation, 7b.2.2
orthogonalization, 31.6.3
orthonormal components, 4b.4.3
orthonormal set, 31.3.3
orthonormalization, 31.6.3
out of the money, 38.4.2
out-of-sample error, 22.236
outputs, 11.1
outstanding order vector, 47.3
overnight index swap, 38.10.2
P
p-value, 30.1.2
p-value test, ??
P&L, 49.1.6
conditional ex-ante, 42.1
pricing function, 42
P&L linearity, 50.1
P&L related exposures, 46c.3
pair-wise Markov property, 15.7
panel data, 22.9
panic copula, 43.7.3
panic drivers, 43.7.3
paper P&L, 50.2.1
par, 38.10.2
par (swap) curve, 38.10.2
par (swap) rate, 38.10.2
par rate, 38.10.2
par swap rate, 38.3.1
parallelogram rule, 31.1.1
parallelotope, 31.2.3
parent, 15.1
parent order, 47
Parseval’s identity, 34.4.3
partial correlation matrix
linear, 4b.2
partial covariance matrix
cross-partial covariance matrix, 4b.2
partial derivative
second order, 32.1.2
vector-valued, 32.59
partial orthogonality, 4b.3
partial standard deviation, 4b.2
partial views, 28.1.4
partition, 32.3.1
encoding, 7b.3.3
partition encoder, 7c.5
partition encoding, 7c.5
partitioned matrix inversion, 31.7.4
path, 31.4.4
payment time, 49.1.3
payoff, 38.4
call option, 38.4.1
forward, 38.2.2
variance swap, 38.4.6
Pearson parametrization
Arrow-Pratt function, 44.5.1
perceptron
perceptron algorithm, 13.1.6
performance "mean", 44.3.1
performance expectation, 44.3.1
performance mean-variance trade-off, 44.3.4
performance model
Black-Litterman, 27.1
performance variance, 44.3.2
permanent impact, 47.1.3
permanent market impact model, 47.1.3
persistence, 46c.3.3
Plancherel theorem, 34.4.3
point view, 28.1.2
point-in-time, 20.3.2
pointed, 33.3.6
Poisson process, 20.1.2, 21.1.3
polarization identity, 31.3.3
pool factor, 49.2.1
pooling
convolution, 26.4.1
portfolio, 43.1
portfolio rebalancing P&L, 50.2.3
portfolio weights, 50.4.2
positive definite, 34.5.2
linear transformation, 3795
positive homogeneity of first degree, 44.2
positive homogenous of degree, 44.2
positive homogenous of first degree, 44.2
positive semidefinite
linear transformation, 3796
posterior, 25.1.2, 25.1.2
Bayesian statistics, 4a.2.2
posterior distribution, 22.8.1
Black-Litterman, 27.25
posterior predictive performance model
Black-Litterman, 27.29
potential function
e-affine coordinates, 3.1.3
m-affine coordinates, 3.1.3
power, 30.1.1
power market impact, 46a.3.3
power spectrum
generalized, 34.6.1
generalized, matrix-valued, 34.6.3
integral, 34.6.1
proper, 34.6.1
proper, matrix-valued, 34.6.3
precision
binary classification, 13.1
precision matrix, 7c.6.1
predicted negative probability, 13.1
predicted positive probability, 13.1
predicted variables, 11.1
prediction, 8.1
error prediction matrix, 16.1.5
linear, 16.1.5
linear mean, 4b.2
linear mean-covariance, 4b.2
mean-covariance, 11.2
point, 11.2
point prediction, 25.3.1
prediction vector, 17.1
predictive distribution, 25.4.1
probabilistic, 11.2
prediction
linear prediction random variable, 16.1.5
prediction model, 22.8.2
predictive, 46a.4.1
predictive distribution, 43.5.1
non-observable, 25.4.1
posterior, 22.8.2
predictor
point, 11.2
point prediction, 25.3.1
predictive distribution, 25.4.1
probabilistic, 11.2
premium, 38.10.2
prevalence of positive outcome, 13.1
price manipulation, 47.5.2
pricing kernel, 37a.2.1
pricing operator, 37a.1.1
pricing signals, 46c.1.2
principal axes, 2b.2.2
principal axis factorization, 8.4.2
principal component analysis, 2b.2.3
sparse principal component analysis, 22.10.6
principal components, 2b.2.3
principal directions, 2b.2.3
principal factors, 2b.2.3
principal root, 31.6.6
principal variances, 2b.2.3
principal-component linear factor model, 8.3
prior
improper, 6.5.2
proper, 6.5.2
prior distribution, 4a.2.2
Black-Litterman, 27.3
prior predictive distribution, 22.8.2
prior predictive performance model
Black-Litterman, 27.8
probabilistic factor analysis, 15.3, 15.3
probabilistic graphical model, 15.1
probabilistic misclassification error, 13.3.1
probabilities, 7c.4
vector, 7c.4
probability density function
multivariate, 2a.1.2
univariate, 2a.1.2
probability distribution function, 7b.1.5
probability integral transform, 5a.1
probability mass function, 2a.1.3
probability of default, 38.5.2
probability space, 7b.1.1
discrete, 7b.1.1
events, 7b.1.1
outcomes, 7b.1.1
probability measure, 7b.1.1
sample space, 7b.1.1
sigma-algebra, 7b.1.1
probit parametrization
binary probit parametrization, 7c.5.2
multinomial probit parametrization, 7c.5.2
probit regression
binary, 13.3.8
process
Gaussian, 16.1.4
product rule
multivariate, 32.1.2
univariate, 32.1.1
profit-and-loss, 49.1.6
projection
i-m-projection, 29.2.1
I-projection, 29.2.1
linear, weak, 4b.4.4
linear-in-features, 12.1.10
m-projection, 29.2.1
projection matrix, 4b.2
projection operator
linear, 4b.2
Projection pursuit, 26.4.3
projection stochastic discount factor, 37a.2.3
properties, 25.1
proportional hazards expectation, 44.8.2
proportional hazards principle, 37c.2.3
proportional hazards transform, 44.8.2
proportional odds, 7c.5.2
pseudo-inverse
left, 31.7.3
right, 31.7.3
pull-to-par, 38.10.2
pure endowment, 37d.4.1
pushforward
distribution, 2a.3.1
put-call parity, 37a.1.2
Pythagorean triangular identity, 31.3.5
Q
quadrangle, 44.4
quadratic discriminant analysis (QDA), 13.3.6
quadratic form
matrix, 31.3.2
quadratic market impact, 46a.3.3
quadratic programming, 33.3.3
quadratic variation, 40.2.3
quadratic-normal distribution, 7c.9.2
quantile
function - univariate, 2a.1.5
functional - univariate, 2a.1.5
multivariate, 4a.4.1, 7a.2.7
multivariate p, 7a.2.7
quantile (VaR) satisfaction measure, 44.6.1, 44.6.1
quantitative alpha, 46c
quantitative strategies, 46c
quotient rule
multivariate, 32.1.2
univariate, 32.1.1
R
r-squared
distributional , 8.1.1
generalized distributional, 8.1.1
generalized population, 8.1.1
population, 8.1.1
sample, 8.1.1
radial component, 7c.2.7
Radon-Nikodym derivative
numeraire, 37a.2.2
process, 37b.4.3
probability spaces, 7b.1.4
rain distribution, 47.5.3
random field, 16.5
covariance stationary, 16.5.1
free field, 16.5.3
continuum, 16.5.3
discrete, 16.5.3
Gaussian, 16.5.5
Gaussian Markov, 15.7
isotropic, 16.5.1
strongly stationary, 16.5.1
random forest, 22.11.1
random matrix, 7b.1.2
random time series, 40
random variable
multivariate, 7b.1.2
univariate, 7b.1.2
random vector, 7b.1.2
random-walk
strong, random-walk-cheat-sheet
weak, 16.2.2
rank
full, 31.2.1
linear transformation, 31.2
matrix, 31.2.1
rank-nullity theorem, 31.2
ranking, 46c.1.5
ranking-distortion, 46c.1.5
ranking-median, 46c.1.5
ranking-terciles, 46c.1.5
real negative probability, 13.1
real positive probability, 13.1
realized information panel, 40
realized P&L, 49.1.6
portfolio, 50.2.1
realized time series, 40
realized variance, 38.4.6
recall, 13.1
receiver operating characteristic (ROC) curve, 13.1.4
receiver operating characteristic (ROC) function, 13.1.4
record date, 49.1.3
recovery rate, 38.5.2
reflection, 31.3.6
regression
cross-section, 8.5.5
discriminative linear regression, 12.3.5
discriminative regression, 12.3.4
generalized, 12.1.2
least absolute deviation regression, 12.2.2
least squares regression, 12.1.2
least squares, linear, 12.1.2
linear least absolute distance regression, 12.2.4
linear median regression, 12.2.4
linear quantile regression, 12.2.4
quantile regression, 12.2.2
regression factor scores, 8.4.4
regression linear factor model, 8.2
regret, 6.1.3, 44.4
excess risk, 6.3.1
regularization, 28.6.6
ridge, 33.4.1
Tikhonov, 33.4.1
reinforcement learning, 11.1.3
reinvested cumulative cash-flow, 49.1.4
reinvested instrument, 49.1.4
reinvestment function, 42.1
rejection region, 30.1.1
relative entropy, 3.1.4, 11.4.1
relative marginal contributions, 45b.2.1
relative score, 7c.5
relative scores, 7c.5.2
relative value,