Optimal investment and consumption for financial markets with jumps
Salle de séminaires M.0.1.
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.