Optimal Portfolio Selection in a Jump-Diffusion Market with both Fixed and Proportional Transaction Costs

摘要

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.