Optimal investment and consumption for financial markets with jumps
Résumé
We consider a portfolio optimization problem for financial markets described by exponential Lévy processes with jumps. For this problem we obtain and study the Hamilton-Jacobi-Bellman (HJB) 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 for find the optimal strategies in the explicit form. Finally, we do the Monte Carlo simulations to illustrate numerically the obtained theoretical results.
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