بهینه سازی ثروت در یک بازار ناقص تحت یک فرآیند پرش نفوذ

We consider a small investor who operates within an incomplete market driven by a diffusion with jumps. His behavior facing the market risks is defined by a utility function. We prove the existence of an optimal portfolio and we characterize this portfolio. The optimal strategy determines a unique equivalent martingale measure which is identified with the Davis’ probability. We find explicit formulae for the optimal portfolio, the wealth and the value function in some particular examples of utility functions. Moreover, we prove that the range of the viable prices is reduced by the use of a utility function. At last, we compare the value function with the value function evalued in a market driven by a continuous asset.