INVESTMENT AND CONSUMPTION IN REGIME-SWITCHING MODELS WITH PROPORTIONAL TRANSACTION COSTS AND

摘要

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 [I]. 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.