Discrete‐time risk sensitive portfolio optimization with proportional transaction costs

Marcin Pitera and Łukasz Stettner

Mathematical Finance, 2023, vol. 33, issue 4, 1287-1313

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.

Date: 2023
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