BFS 2002

Poster Presentation

On the dynamical programming equation of risk sensitive control problem associated to an optimal investment model

Shuenn-Jyi Sheu, Hidehiro Kaise

We consider an investment model proposed by Bielecki and Pliska. The prices of securities we can invest in the market are affected by some economic factors which evolve as a diffusion process. The goal is to maximize the expected utility in infinite time horizon. We assume that the utility function is HARA, then we can use dynamical programming approach to derive the Bellman equation which is a nonlinear partial equation. It is important to study this equation, since for each solution there associates a candidate of optimal investment policy. We study the structure of the solutions of this equation. We can obtain a special solution which is relevant to the investment problem. Our approach is different from the conventional one that we do not need to introduce function spaces in the argument.