Abstract
In this paper, we study the optimization problems of minimization of shortfall risk under the jump diffusion model. Jump-diffusion asset price model is driven by nonexplosive counting process that is more general than Poisson process. We take the expected discount utility of shortfall risk as our objective function. Applying Legendre transform and stochastic analysis methods,the existence of equivalent martingale measure and the optimal portfolio is proved. Furthermore, the value function, the optimal portfolio, and the optimal terminal wealth are also proposed.
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