BFS 2002

Contributed Talk

Risk sensitive portfolio optimization with transaction costs

Stanley Pliska, Tomasz Bielecki, Jean Philippe Chancelier, Agnes Sulem

We develop methods of risk sensitive impulsive control theory in order to solve an optimal asset allocation problem with transaction costs and a stochastic interest rate. The optimal trading strategy and the risk-sensitized expected exponential growth rate of the investor's portfolio are characterized in terms of a nonlinear quasi-variational inequality. This problem can then be interpreted as the ergodic Isaac-Hamilton-Jacobi equation associated with a min-max problem. We use a numerical method based on an extended two-stage Howard-Gaubert algorithm and provide numerical results for the case of two assets and one factor that is a Vasicek interest rate.