Discrete-time risk sensitive portfolio optimization with proportional transaction costs

TL;DR

This paper develops a framework for discrete-time risk-sensitive portfolio optimization considering proportional transaction costs, providing theoretical solutions and numerical methods to improve trading strategies under risk preferences.

Contribution

It introduces a Bellman equation approach for optimal strategies in risk-sensitive portfolio management with transaction costs, under minimal assumptions.

Findings

Existence of solutions to the Bellman equation under minimal assumptions

Characterization of optimal strategies for risk-averse and risk-seeking investors

Numerical examples demonstrating strategy refinement using Bellman analysis

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.