Stochastic Optimal Control of Investment-Consumption Models

The aim of this project is to determine investment strategies for risky assets that maximize the expected utility of wealth or consumption of an investor. We assume that the investor can allocate his wealth between a risky asset and a savings account. Due to the empirically detected discontinuous price evolution in recent years, and due to turbulence on the financial markets, we model the price of the risky asset as a stochastic process that jumps downwards at an uncertain moment with an uncertain height. (Market crash modeling by Korn/Wilmott (2001)). Additionally, the interest rate of the savings account is modeled as a stochastic process.

The investor’s wealth is controlled by the choice of the investment strategy that describes the fraction of wealth invested in the risky asset. The aim is to determine a strategy that maximizes the expected utility of wealth or consumption in the worst-case scenario. The resulting control problem should be solved explicitly by methods of stochastic optimal control.

• Martin Luther University Halle-Wittenberg (MLU), Institute for Mathematics