Long-run risk-sensitive portfolio optimisation with proportional transaction costs and log Lévy asset prices

Damian Jelito, Łukasz Stettner

Abstract

We study a long-run risk-sensitive portfolio problem with proportional transaction costs in a continuous-time market whose log-prices are given as a Lévy process, and rebalancing is possible only at random moments of investment opportunities. Using a Schauder fixed-point argument, we solve the ergodic Bellman equation without any mixing assumptions. Under additional full-support and growth conditions, the solution to the Bellman equation is unique, with the unique continuous maximiser. We also prove vanishing risk-aversion asymptotics towards the risk-neutral (Kelly) problem and convergence of a dyadic-time-grid approximation of the random intervention moments. Numerical examples illustrate the results.

Disclosure

“ηim ] for different m. Declaration of generative AI use During the preparation of this work, the authors used large language model assis- tants to support proof idea generation, proofreading, and code writing for numerical examples. All AI-assisted output was used under supervision: the authors verified every derivation and numerical result and edited the text as need”
PDF page 36

Classification: Proof ideas or individual proof-step assistance
Multiplier: 8
Verified: 2026-08-22T18:27:12.403730Z

Structural counts

Pages 36 pdf

Theorems 8 source

Lemmas 11 source

Propositions 2 source

Corollaries 2 source

Definitions 0 source

Displayed equations 170 source

Bibliography entries 0 source

Appendix pages 0 estimated

Count notes

Source counts use the expanded primary TeX file main_arxiv.tex.
Appendix pages include the first PDF page with an explicit Appendix heading through the final page.