Discrete‐time risk sensitive portfolio optimization with proportional transaction costs

Abstract

Abstract In this paper we consider a discrete‐time risk sensitive portfolio optimization over a long time horizon with proportional transaction costs. We show that within the log‐return i.i.d. framework the solution to a suitable Bellman equation exists under minimal assumptions and can be used to characterize the optimal strategies for both risk‐averse and risk‐seeking cases. Moreover, using numerical examples, we show how a Bellman equation analysis can be used to construct or refine optimal trading strategies in the presence of transaction costs.