The Theory channel of the ARPM Lab is a 2,000+ page-long encyclopedia of advanced data science and modern quantitative finance.
Math primer
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MathematicsPrimers of linear algebra, calculus, functional analysis and optimization, to master the mathematical foundations of Quantitative Finance. |
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Static and dynamic models for multivariate randomness
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StatisticsThorough coverage of distributions, copulas, location and dispersion features, correlation and statistical decision theory, to understand and model multivariate randomness. |
Factor models and machine learningIn-depth treatment of linear factor models, and generalizations to supervised and unsupervised machine learning models, for point and probabilistic prediction. |
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Stochastic processesDefinition 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. |
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Data and Views
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EstimationNon-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 |
InferenceConditioning, Black-Litterman, relative entropy minimization and generalized approaches to inject information and subjective views in the estimation, portfolio allocation, and other decision making processes |
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).
ValuationHolistic 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. |
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The “Checklist”: Ten steps for Advanced Risk and
Portfolio Management
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Data processingFive 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 managementThree 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. |
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Portfolio managementTwo 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). |
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Performance analysisEx-post attribution of the realized performance to different decisions and stakeholders |