Utility maximization of the exponential Lévy switching models

Yu. Dong^a, L. Vostrikova<sup>b

a</sup> National University of Singapore, Institute of Operations Research and Analytics, Singapore
^b LAREMA, Département de Mathématiques, Université d'Angers, France

Abstract: This article is devoted to maximization of HARA (hyperbolic absolute risk aversion) utilities of the exponential Lévy switching processes on a finite time interval via the dual method. The description of all $f$-divergence minimal martingale measures and the expression of their Radon–Nikodým densities involving the Hellinger and Kulback–Leibler processes are given. The optimal strategies in progressively enlarged filtration for the maximization of HARA utilities as well as the values of the corresponding maximal expected utilities are derived. As an example, the Brownian switching model is presented with financial interpretations of the results via the value process.

Keywords: Lévy switching models, utility maximization, dual approach, $f$-divergence minimal martingale measure, optimal strategy.

Received: 19.10.2020
Revised: 13.05.2023
Accepted: 13.10.2023

DOI: 10.4213/tvp5445

 English version: Theory of Probability and its Applications, 2024, 69:1, 127–149

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