Optimal Consumption and Portfolio in a Jump Diffusion Market with Proportional Transaction Costs
Abstract
We study the optimal consumption and portfolio in a jump diffusion market with proportional transaction costs. We show that the solution in the jump diffusion case has the same form as in the pure diffusion case; in particular, (under some assumptions) there is a transaction cone D such that it is optimal to make no transactions as long as the wealth position remains in D and to sell/buy stocks according to local time on the boundary of D. The associated integro-differential variational inequality is studied by using the theory of viscosity solutions.