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The research monograph Stochastic Portfolio Theory by E. R. Fernholz presents a novel mathematical methodology for analyzing portfolio behavior and stock market structure. Stochastic portfolio theory is descriptive rather than normative, and hence it differs from the current doctrine of mathematical and quantitative finance. Descriptive theories offer explanations for observed phenomena and predictions for the outcomes of future experiments; the theories of natural science are descriptive theories. The central theories of finance are normative theories: general equilibrium, dynamic asset pricing, no-arbitrage. These normative theories are based on assumed ideal behavior regarding the interaction of the participants and agents in the markets under consideration, and this ideal behavior is frequently far different from actual observed behavior.
