Optimal consumption and portfolio in a jump diffusion market with proportional transaction costs

We consider the problem of optimal consumption and portfolio in a jump diffusion market in the presence of proportional transaction costs for an agent with constant relative risk aversion utility. We show that the solution in the jump diffusion case has the same form as in the pure diffusion case first solved by Davis and Norman [Mathematics of Operations Research 15 (1990) 676-713]. In particular, we show that (under some assumptions) there is a no transaction cone D in the (x, y)-plane 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. (C) 2001 Elsevier Science B.V. All rights reserved.