Abstract:  

These lectures survey the foundations and recent developments of Stochastic Portfolio Theory (SPT), introduced by E.R. Fernholz in the 1990’s, is a rich and flexible framework for analyzing portfolio behavior and equity market structure. It has been further  developed at vigorous clip since then.  As a theoretical tool, the framework of SPT offers fresh insights into questions of  market structure and arbitrage, and can be used to construct portfolios with controlled behavior. As a practical tool, it has been applied to the analysis and optimization of portfolio performance and has been the basis of successful investment strategies. 

References

• E.R. FERNHOLZ and I. KARATZAS (2009)  Stochastic Portfolio Theory: an overview.in: A Bensoussan & Q Zhang (eds): Hanbdoo k of Numerical Analysis: Special Volume on Mathematical Modeling in Finance, Elsevier, pages 89-168.
• E.R. FERNHOLZ, I. KARATZAS & C. KARDARAS (2005) Diversity and arbitrage in financial markets. Finance & Stochastics 9, 1-27.
• A. BANNER, E.R. FERNHOLZ & I. KARATZAS (2005) Atlas models of equity markets. Annals of Applied Probability 15, 2296-2330.
• E.R. FERNHOLZ & I. KARATZAS (2005) Relative arbitrage in volatility-stabilized markets. Annals of Finance 1, 149-177.
• T. ICHIBA, V. PAPATHANAKOS, A. BANNER, I. KARATZAS  &  E.R. FERNHOLZ  (2011)  Hybrid Atlas Models.  Annals of Applied Probability  21, 609-644.