Some stability results of optimal investment in a simple Lévy market

We investigate some investment problems of maximizing the expected utility of the terminal wealth in a simple Lévy market, where the stock price is driven by a Brownian motion plus a Poisson process. The optimal investment portfolios are given explicitly under the hypotheses that the utility functions belong to the HARA, exponential and logarithmic classes. We show that the solutions for the HARA utility are stable in the sense of weak convergence when the parameters vary in a suitable way.