Investment and consumption in regime-switching models with proportional transaction costs and log utility

A continuous-time and infinite-horizon optimal investment and consumption model with proportional transaction costs and regime-switching was considered in Liu [ 4 ]. A power utility function was specifically studied in [ 4 ]. This paper considers the case of log utility. Using a combination of viscosity solution to the Hamilton-Jacobi-Bellman (HJB) equation and convex analysis of the value function, we are able to derive the characterizations of the buy, sell and no-transaction regions that are regime-dependent. The results generalize Shreve and Soner [ 6 ] that deals with the same problem but without regime-switching.