On convergence to the exponential utility problem with jumps

We derive an explicit portfolio for the exponential utility maximization problem via an approximation approach for exponential Levy processes (mainly discussing -e(-x) (exponential problem) and -(1-x/2m)(2m)) (2m-th problem)). A result by Jeanblanc et al. (Annals of Applied Probability, 2007) is applied: The convergence of q-optimal martingale measures to the minimal entropy martingale measure. Except for conditions on the existence of the q-optimal measures, we replace technical assumptions by minor integrability conditions. We obtain convergence of the portfolios of the 2m-th to the exponential problem. The influence of jump intensity and jump size distribution upon the portfolio, in comparison to the continuous case, is discussed.