Laboratoire de Mathématiques Raphaël Salem

UMR 6085 CNRS - University of Rouen Normandy

We consider a portfolio optimization problem  for financial markets described by exponential Levy processes with jumps. For this problem we obtain and study the Hamilton-Jacobi-Bellman equation which is an integral and partial differential equation of the second order. For this problem we show the corresponding verification theorem and construct the optimal  consumption/investment strategies. For the power utility function we find the optimal strategies in the explicit form. Finally, we do the Monte Carlo simulations to illustrate numerically the obtained theoretical results.