Probabilistic and Stochastic perspectives on instantaneously rebalanced portfolio strategies

Abstract: In this talk we describe the basic ideas of Stochastic Portfolio Theory used to describe the value process of instantaneously rebalanced portfolio strategies in a market based on a Brownian log-price process, and then give some more naive probabilistic approaches for describing this value process by taking a limit of discretely rebalanced portfolio strategies.  Throughout we will focus on the simplest possible example of an antisymmetric two stock market to easily visualize the main ideas and techniques, which allow one to consider markets based on more general non-Brownian price processes.