CAREER: Stochastic Control Problems in Financial Engineering

University Of California-Berkeley, Berkeley CA

Investigators

Abstract

The objective of this Early Faculty Career Development (CAREER)research is to understand and solve stochastic control problems of contemporary interest in finance. There are two broad directions of research. The first concerns the analysis of structural properties of optimal investment and hedging portfolios when there are stochastic parameters and discontinuities in the underlying asset price models. This issue will be studied using methods from stochastic control, stochastic differential equations, and stochastic analysis. Numerical methods, possibly using simulation together with a finite dimensional approximation that exploits the structure of the optimal solution, will be explored. The second objective concerns the analysis of multi-period investment policies that are robust with respect to errors in the underlying financial model. This analysis will be carried out using results from convex optimization and stochastic control. The primary goal of this research is to understand the structural properties of robust portfolios, that is, investment portfolios that perform well in the real world even when there are errors in the underlying model being used to make decisions, and to develop numerical methods for computing them. More generally, the objective is to develop analytical methods for understanding the structural properties of robust decisions for general dynamic optimization problems. If successful, the results of this research will lead to an improved understanding of the structural properties of optimal investment and hedging decisions associated with financial models involving stochastic parameters, jumps, and default risk. Empirical results indicate that these are significant sources of risk that should not be ignored, and successful completion of this research will lead to a more complete understanding of the appropriate response to such sources of risk, and efficient numerical methods for computing these decisions. For the problem of robust investment, this research will lead, if successful, to a better understanding of the structure of investment portfolios that perform well in the real world, even when there are errors in the underlying mathematical model, and more generally, to greater insight into the impact of model uncertainty and modeling errors on decision making for general multi-period problems. The proposed research will also contribute to numerical methods for computing robust optimal decision policies.