Advanced Stochastic Portfolio Theory in Mathematical Finance

Abstract

his lecture notes summarizes standard machinery of an advanced course on Stochastic Portfolio Theory, presents techniques for analysis of portfolio dynamics and equity market structure. This notes is based on material developed in a series of papers published in recent years by Prof. Ioannis Karatzas and his lectures regularly given at Columbia University in the city of New York.

It gives introduction to a number of questions of market structure and arbitrage, used to construct portfolios controlled behaviour. The Stochastic Portfolio theory has been applied to analysis and optimization of portfolio performance and denotes a benchmark portfolio performance and successful investment strategies.