ARPM Lab - Theory

The Theory channel of the ARPM Lab is a 2,000+ page-long encyclopedia of advanced data science and modern quantitative finance.

Data Science

The ARPM Lab covers the following areas.

Math primer	Mathematics Primers of linear algebra, calculus, functional analysis and optimization, to master the mathematical foundations of Quantitative Finance.
Static and dynamic models for multivariate randomness	Statistics Thorough coverage of distributions, copulas, location and dispersion features, correlation and statistical decision theory, to understand and model multivariate randomness.
Factor models and machine learning In-depth treatment of linear factor models, and generalizations to supervised and unsupervised machine learning models, for point and probabilistic prediction.
Stochastic processes Definition and properties of the most common mean-covariance and probabilistic processes, to model the dynamics of continuous and discrete-state variables, in continuous and discrete time.
Data and Views	Estimation Non-parametric, parametric, Bayesian, robust and shrinkage estimation techniques, to fit models to data in a meaningful way; estimation assessment methods, to optimize the bias-variance trade-oﬀ
Inference Conditioning, Black-Litterman, relative entropy minimization and generalized approaches to inject information and subjective views in the estimation, portfolio allocation, and other decision making processes

Math primer

Mathematics

Primers of linear algebra, calculus, functional analysis and optimization, to master the mathematical foundations of Quantitative Finance.

Static and dynamic models for multivariate randomness

Statistics

Thorough coverage of distributions, copulas, location and dispersion features, correlation and statistical decision theory, to understand and model multivariate randomness.

Factor models and machine learning

In-depth treatment of linear factor models, and generalizations to supervised and unsupervised machine learning models, for point and probabilistic prediction.

Stochastic processes

Definition and properties of the most common mean-covariance and probabilistic processes, to model the dynamics of continuous and discrete-state variables, in continuous and discrete time.

Data and Views

Estimation

Non-parametric, parametric, Bayesian, robust and shrinkage estimation techniques, to fit models to data in a meaningful way; estimation assessment methods, to optimize the bias-variance trade-oﬀ

Inference

Conditioning, Black-Litterman, relative entropy minimization and generalized approaches to inject information and subjective views in the estimation, portfolio allocation, and other decision making processes

Quantitative Finance

While most materials on Quantitative Finance focus on asset pricing and risk neutral valuation (“Q”), the ARPM Lab focuses on the much broader applications to real world probability (“P”, learn more).

	Valuation Holistic treatment of valuation methods across liquidity buckets: bid/ask or mark-to-market versus mark-to-model; and across models: risk-neutral models for derivative traders versus real-measure models for investment bankers and actuaries.
The “Checklist”: Ten steps for Advanced Risk and Portfolio Management	Data processing Five steps to map past raw market data into the distribution of the market over a future investment horizon, by means of advanced econometric, estimation and financial engineering techniques.
Risk management Three steps to assess the risk profile of a portfolio/firm, by means of risk measures, ex-ante risk/performance attribution models, and advanced stress-testing techniques.
Portfolio management Two steps to optimize the risk profile of the portfolio/firm, which is the ultimate goal of financial practitioners across the industry (asset management, banking, insurance).
	Performance analysis Ex-post attribution of the realized performance to diﬀerent decisions and stakeholders

Valuation

Holistic treatment of valuation methods across liquidity buckets: bid/ask or mark-to-market versus mark-to-model; and across models: risk-neutral models for derivative traders versus real-measure models for investment bankers and actuaries.

The “Checklist”: Ten steps for Advanced Risk and Portfolio Management

Data processing

Five steps to map past raw market data into the distribution of the market over a future investment horizon, by means of advanced econometric, estimation and financial engineering techniques.

Risk management

Three steps to assess the risk profile of a portfolio/firm, by means of risk measures, ex-ante risk/performance attribution models, and advanced stress-testing techniques.

Portfolio management

Two steps to optimize the risk profile of the portfolio/firm, which is the ultimate goal of financial practitioners across the industry (asset management, banking, insurance).

Performance analysis

Ex-post attribution of the realized performance to diﬀerent decisions and stakeholders