Approximating Optimal Trading Strategies Under Parameter Uncertainty: A Monte Carlo Approach

Abstract

This paper considers the problem of a capital-limited investor with log utility who has the opportunity to invest in a security that follows a parametric price process. While the investor knows the form of the process, the exact parameter values are not known and must be inferred by observing the evolution of the security's price over time. The paper describes an investment approach based on Monte Carlo simulations and particle filters that allows the investor to approximate an optimal trading strategy while explicitly incorporating parameter uncertainty into the investment decision. The approach is applicable to any model and to single or synthetic securities.