Optimal portfolio selection in a jump-diffusion market with both fixed and proportional transaction costs

The optimal portfolio selection problem for a constant relative risk averse (CRRA) investor who faces fixed and proportional transaction costs and maximizes the total expected utility of consumption over a planning horizon is considered. We use a continuous-time model with one riskless and one risky asset, in which the price of the risky asset is governed by jump-diffusion process. This problem is formulated as a combined stochastic control and impulse control problem whose solution is obtained by using Quasi-Variational Inequlities (QVI). Some properities of the value function of this problem are also discussed.