Glossary

Symbols

(functional) excess risk, 16
0-1 loss, 13.1.2

Wiener-Kolmogorov filter
    non-causal, 31.6.1

A

absence of arbitrage, 41a.1.3
absolute score, 39.6, 39.6
absolutely continuous component, 31.1.2
absolutely continuous spectral density, 31.1.2
abstract Bayes theorem, 38.3.5
acceptance region, 22.1.1
accounting signals, 50c.1.4
accrued interest, 55.1.3
accuracy
    binary classification, 13.4
action, 6b.1.2
    Bayes, 6b.3.1
    minimax, 6b.4.1
action space, 6b.1.2
activation function, 16.4.1
activity time, 42.8.1
actual cash-flow, 54.8.3
actual exchange rate, 54.8.3
actual value, 54.8.3
adapted basis, 33.1.3
adaptive execution algorithm, 51.3.2
additive, 39.9.2
admissible, 17.8.1
affine concordance
    negative, 5a.3
    positive, 5a.3
affine transformation, 2a.3
algebraic multiplicity, 33.9.1
algebraic Riccati equation, 33.6.6
allocation policy, 47.5
almost everywhere
    function equality, 36.3.1
alpha, 48.3.1
    binary classification, 13.1
alternative beta, 50c
alternative hypothesis, 22.3
analysis of variance, 3b.7.4
ancestor, 15.1
angle, 33.3.3
    canonical, 38.2.4
anti-monotonic
    function, 34.4.3
approximation-estimation trade-off, ??
Arbitrage, 41a.16
arbitrage pricing theory, 41b.3.1
architecture, 16.4.1
area under curve (AUC), 13.1.4
arithmetic Brownian motion with drift, 32.1.2
Arrow-Debreu securities, 41b.1.2
Arrow-Pratt absolute risk aversion function, 48.5.1
ask size, 53.4.1
assets, 47.7.1
at the money, 55.2.1
    foreign exchange market, 42.4.3
augmented view variables, 25.5.3
autocorrelation
    function, 27.4.1
    partial autocorrelation function, 27.4.1
autocovariance
    partial autocovariance function, 27.4.1
autocovariance function, 27.1
    random field, 27.4.2
autoencoder, 14.1
autoregressive conditional duration, 43.5.3
autoregressive fractionally integrated moving average, 43.3
autoregressive moving average process
    autoregressive
        multivariate (VAR), 29.3.1
        univariate (AR), 29.3.1
    autoregressive polynomial, 29.3.1
    companion matrix, 29.3.1
    integrated
        multivariate (VARIMA), relationships-varma-vma-var
        univariate (ARIMA), 29.4
    invertible, 29.3.3
    LTI filter representation, 29.3.1
    moving average
        mutivariate (VMA), 29.3.1
        univariate (MA), 29.3.1
    moving average polynomial, 29.3.1
    multivariate (VARMA), 29.3.1
    univariate (ARMA), 29.3.1
    Yule-Walker equation
        univariate, sec-covstat-arma
autoregressive of order one
    Gaussian, 29.2.5
    univariate (AR), 29.2.1
    vector (VAR), 29.2.1
auxiliary measure, 39.7

B

Bachelier, 41d.2.1
backpropagation, 16.4.1, 35.2.3
backward cash-flow-adjusted value, 53.3.4
backward/forward exponential weighted moving average, 17.12.3
bagging, 17.11.1
balance sheet, 47.7.1
balanced, 17.9
bandpass filter, 31.2.4
bandwidth, 17.1.2
    kernel density estimate, 17.3
bandwidth matrix, 17.1.2
base case, 25.6.1
base distribution, 25.1.1
base measure, 39.7
basis, 33.1.2, 54.5.3
    canonical, 33.1
    orthonormal, 33.3.4
basis denominator, 54.5.3
basis instruments, 41b.1.1
Bayes classifier, 13.2.3
Bayes risk
    of a decision, 6b.3.4
    of an action, 6b.3.1
Bayes theorem, 3b.3.1
Bayesian networks, 15.6
benchmark, 54.6.1
Bernoulli distribution, 39.6
best approximation
    linear, 3a.2.1
best ask, 53.4.1
best bid, 53.4.1
best prediction, 33.3.5
beta
    binary classification, 13.1
beta conditions
    projection coefficients, 33.3.4
    projection equation, 33.3.4
beta distortion index, 48.8.2
beta-adjusted excess return, 54.6.2
bets, 49b.4
between-cluster/group variance, 3b.7.4
Bhattacharyya coefficient, 17.11.4
bias, 20.1.1
    binary classification, 13.1
bias-variance trade-off, 21.3.2
bid size, 53.4.1
bid-ask spread, 51.1
bilateral value adjustment, 47.2
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, 39.6
binning, 42.8.2
binomial inverse theorem, 33.7.4
binomial tree, 43.1.2
bins, 39.5.1, 42.8.2
Black-Merton-Scholes model, 41d.2.2
block-wise orthogonality
    partial, 3a.5
Bochner’s theorem, 36.6.1
bond yield, 46.3.2
bootstrap aggregating, 17.11.1
Borel sets, 38.1.2
boundedness, 25.1.7
breadth, 16.4.1, 50a.4.4
breakdown point, 17.7.2
Brier scoring rule, 13.3.1
Buhlmann pricing equation, 41a.5
    expectation, 41a.5
Buhlmann principle, 41c.2.4
butterfly, 41b.1.2, 42.4.3

C

calendar signal, 50c.1.4
calibrate, 41d
call option
    European, 55.2.1
        expiry time, 55.2.1
        strike, 55.2.1
calm drivers, 47.6.3
canonical correlation matrix, 5a.4
canonical parameters, 39.7
capital asset pricing model, 41b.2
capital gain, 54.1.1
cardinality, 36.1.2
cardinality constraint, 35.5, 37.2
carry signal, 50c.1.1
CART, 16.3.1
cash-flow function, 46.1
cash-flow-adjusted value, 53.3.4
categorical distributions, 39.6
categories, 39.6
Cauchy distribution, 39.4.3
Cauchy transform, 2b.1.5
Cauchy-Schwarz inequality, 33.3.3
causal, 31.2.4
central tendency, 7.2.1
    affine equivariant, 7.1.1, 7.1.4
certainty-equivalent, 48.5
certainty-equivalent principle, 41c.2.2
chain rule
    gradient, 34.1.2
    matrix-variate, 34.1.3
    multivariate, 34.1.2
    univariate, 34.1.1
change of variable formula
    multivariate, 34.3.4
    univariate, 34.3.2
Chapman-Kolmogorov equations, 30.2
characteristic equation, 33.5.1
characteristic function, 2b.1.4
characteristic matrix, 50c.5.1
characteristic polynomial, 33.5.1
characteristic portfolio, 50c.3.1
characteristic portfolios, 50c.5.1
Chebyshev’s inequality, 2a.4.2
chi-squared distribution, 39.3.1
    generalized, 39.3.3
child, 15.1
child orders, 51
Cholesky decomposition, 33.6.5
    upper, 33.6.5
Cholesky root
    lower triangular, 33.6.5
    upper triangular, 33.6.5
CIR, 32.2.2
claims, 42.6
classes, 39.6
classical-equivalent, 17.8.1
classification
    discriminative classification, 13.3.5
    multinomial classification, 13.2
classification and regression trees, 16.3.1
clean price, 55.1.3, 55.1.3
clique, 15.1
    maximal clique, 15.1
clique factorization, 15.7
clustering, 14.1.2
co-monotonic
    function, 34.4.3
    pair of vectors, 5b.3.3
co-monotonic additivity, 48.2
co-variogram
    random field, 38.1.4
coalition, 37.2
codes, 14.1
coherent satisfaction measure, 48.9.1
    coherent probability measure, 48.9.1
    worst case expectation representation, 48.9.1
cointegrated space, 43.7.1
cointegration signal, 50c.1.3
cointegration vector, 43.7.1
collateral, 47.8.3
combination, 37.2
combinatorial heuristic, 37.2.6
    2-step forward, 37.2.4
    naive selection, 37.2.2
    stepwise backward elimination, 37.2.4
    stepwise bidirectional elimination, 37.2.4
    stepwise forward selection, 37.2.3
combinatorial programming, 37.2
commonalities, 8.4.5
comparable instruments, 41d
complete, 41b.1.1
complete class theorem, 6b.3.6
complete metric space, 36.3.1
compound distribution, 3b.3.1
compound Poisson process, 32.1.3
compounded rate of return
    (instantaneous) compounded rate of return, 54.5.6
    average compounded rate of return, 54.5.6
compounded return, 54.5.1
Comprehensive Capital Analysis and Review, 47.6
concave down function
    univariate, 34.5.1
concave function
    multivariate, 34.5.2
    univariate, 34.5.1
concave up function
    univariate, 34.5.1
concavity, 48.2
condition number, 18.6.2
conditional cdf, 3b.2.1
conditional covariance, 3b.7.3
conditional excess distribution, 48.6.2
conditional expectation
    Stochastic processes, 28.4.1
    with respect to partition, 38.3.3
conditional independence, 3b.5, 17.9
conditional mean, 3b.7.2
conditional mean estimator
    square bias, 21.3.2
    variance, 21.3.2
conditional median, 3b.7.5
conditional mode, 3b.7.1
conditional pdf, 3b.2.1
conditional pmf, 3b.2.1
conditional principal component analysis, 8.6.16
conditional principal directions, 8.6.16
conditional principal variances, 8.6.16
conditional probability, 38.1.8
    with respect to partition, 38.3.2
conditional quantile, 3b.7.5
conditional value at risk, 48.8.2
conditioning-marginalization, 25.1.3
cone, 35.3.6
confidence, 22.1.1
confusion matrix, 13.1
conic programming, 35.3.6
conjugate distribution, 17.8.3
consistency with weak dominance, 48.2
consistent with q-th order dominance, 48.2
constancy, 48.2
constant proportion portfolio insurance, 50d.4.1
constraint set, 35.1.1
    selection, 35.5
contingency table, 13.2.1
continuous-state distributions, 43.1
control variable, 11.1.3
convex function
    multivariate, 34.5.2
    univariate, 34.5.1
convex programming, 35.3
    epigraph form, 35.6.2
convex set, 34.5.2
convexity, 46.3.2, 46.3.2
    effective key-rates, 46.3.2
    risky investment, 50d.6
    satisfaction/risk measures, 48.2
convolution, 36.4.3
    cyclic, 36.4.7
    discrete, 36.4.5
    integral, 36.4.4
    periodic, 36.4.6
convolution theorem, 36.4.3
coordinate descent, 35.5.4
Copula
    independence copula, 5b.3.1
copula, 5b.3
    Archimedean, 5b.5
    elliptical, 5b.4
    pdf, 5b.2
copula-marginal combination, 5b.6.2
copula-marginal distributions, 5b.6.2
copula-marginal separation, 5b.6.1
Cornish-Fisher approximation, 48.6.2
Cornish-Fisher expansion, 48.6.2
correlation, 5a.2
correlation function, 5a.2
correlation matrix, 5a.2
cost of equity, 41d.1.1
cost of trading, 50d.6
counterparty credit risk, 47.2
coupling function, 3b.4.2
    linear, non-standardized, 3a.4.1
coupon bond, 55.1.3
CoVaR, 47.6.1
covariance
    abstract, 38.2.1
covariance inner product
    multivariate, 38.2.6
    univariate, 38.2.6
covariance matrix, 2a.1.2
    cross-covariance, 2a.1.2
    partial, 3a.2.1
covariance principle, 41a.5
covariant, 4.1.1
covariates, 11.1
Cramer decomposition, 31.1.2
Cramer-Lundberg ruin model, 47.7.5
credit ratings, 42.5.2
credit structural model, 42.5.1
credit value adjustment , 47.2
critical point, 35.2.1
critical region, 22.1.1
cross the spread, 51.1
cross-autocorrelation
    function, 27.4.1
cross-autocovariance
    function, 27.1, 27.2
cross-entropy, 11.4.1
cross-sectional, 50c, 50c
cross-sectional linear factor model, 8.5
cross-sectional sample median of default probabilities, 42.5.2
cross-spectral density, 31.1.2
cumulant , 45.7.1
cumulative cash-flow, 53.3
cumulative distribution function, 2b.1.1
cumulative link, 39.6.2
cumulative monetary amount, 53.4.1
cumulative number of migrations, 42.5.2
cumulative P&L, 42.9
cumulative signed volume, 53.4.1
cumulative trade sign, 53.4.1
cumulative volume, 53.4.1
currency carry trade, 46.2.2
curvature, 42.3.4
curve, 33.4.4
curve/surface signals, 50c.1.4
cutoff classifier, 13.1.4

D

data, 17.4.1, 21.3
data-generating process, 6b.1.1
debt, 47.7.1
debt value adjustment, 47.2
decay, 42.3.4
decision
    deterministic, 6b.3
decision function
    admissible, 6b.3.6
    Bayes, 6b.3.4
    minimax, 6b.4.1
    optimal posterior, 6b.3.3
    randomized, 6b.3
decision problem
    statistical, 6b.1
decision region
    binary classification, 13.2.3
decision regions
    multinomial classification, 13.2
decoder, 14.1
decreasing function, 34.4.1
    entrywise, 34.4.2
    matrix-valued, 34.4.2
    strictly, 34.4.1
degree of reversal, 50c.3.4
delta, 42.4.3
delta p, 13.4
delta rule, 16.4.1
dependent variables, 8.1, 11.1
depth, 16.4.1
derivative, 55.2
    Asian-style, 55.2A
    directional, 34.1.2
    European-style, 55.2
        expiry, 55.2
    first, 34.1.1
    higher order, 34.1.1
    partial, 34.1.2
    second, 34.1.1
    total, 34.1.2
    univariate, 34.1.1
descendant, 15.1
design of experiments, 11.1.3
determinant, 33.2.3
deviation
    expectile, 7.2.3
    maximum, 7.2.4
    mean absolute, 2b.4.3
    median absolute, 2b.4.3
    subquantile, 7.2.3
differentiable function
    multivariate, 34.1.2
    univariate, 34.1.1
Differential entropy, 11.4.1
dimension, 33.1.2
Dirac delta, 36.3.2
direct sum, 33.1.3
directed graph, 15.1
dirty price, 55.1.3
discount, 55.1.3
discount factor, 54.8.3
discount function, 46.1
discounted cash-flow, 41d.1.1
discounted cash-flow adjusted value, 41c.3.1
discounted payoff, 41c.2
discrete derivative
    central first order, 37.1.1
    central second order, 37.1.1, 37.1.2
discrete distribution, 2b.1.3
discrete Laplacian, 37.1.2
discrete-state distributions, 43.1
discrete-state random walk, 43.1.2
discriminant variables, 39.6
discriminative model, 11.2.2
    generative embedding, 11.2.2
discriminative next-step model, 43.6.6
dispersion, 7.2.1
    affine equivariant, 7.1.1
distance, 33.4.2
    absolute, 33.4.2
    Euclidean, 33.3.3
    identity of indiscernibles, 33.4.2
    Lp, 36.3.5
    Mahalanobis, 33.4.2
    p, 33.4.2
    subadditivity, 33.4.2
    symmetry, 33.4.2
    triangle inequality, 33.4.2
distance matrix, 13.2.1
distance to default, 43.4.3
distorted cdf
    satisfaction indices/risk measures, 48.8.1
distorted pdf
    satisfaction indices/risk measures, 48.8.1
distortion function, 48.8.1
distortion principle, 41c.2.3
distortion satisfaction measure, 48.8.1
distribution
    (absolutely) continuous, 2b.1.2
    mixed, 2b.1.1
distributional view, 25.1.3
divergence, 33.4.3
    Bregman, 33.4.3
    difference, 33.4.3
    extended f, 33.4.3
    identity of indiscernibles, 33.4.3
    separable, 33.4.3
diversification distribution, 49b.4
diversity, 17.11.4
dividend-adjusted value, 42.1
    stocks, 53.3.4
divisors, 39.9.3
dollar duration, 53.1.4
dollar-neutral constraint, 50c.3.3
domain
    circle, 36.1.1
    continuous, 36.1.1
    cyclic group, 36.1.1
    discrete, 36.1.1
    frequency, 36.4
    space, 36.4
    time, 36.4
    torus, 36.1.1
dominant-residual LFM, 8.1.2
dot product, 33.3
drawdown, 54.7
    maximum (absolute) drawdown, 54.7
    maximum percentage drawdown, 54.7
    percentage drawdown, 54.7
dual Legendre, 4.1.3
dually flat, 4.1.3
duration, 46.3.2
    effective key rates, 46.3.2
DV01, 53.1.4
dynamic allocation, 50c
dynamic conditional correlation, 44.1.3
dynamic linear factor model, 31.6
dynamic principal component, 31.6.2
dynamic regression linear factor model, 31.6.1