Utility maximization for L{\'e}vy switching models

TL;DR

This paper develops a dual approach to maximize HARA utilities in Lévy switching models, characterizing optimal strategies and minimal martingale measures, with an illustrative Brownian switching example.

Contribution

It provides a comprehensive description of f-divergence minimal martingale measures and explicit optimal strategies in Lévy switching models using dual methods.

Findings

Explicit formulas for Radon-Nikodym densities involving Hellinger and Kullback-Leibler processes

Characterization of optimal strategies in enlarged filtrations

Application to Brownian switching model with financial interpretation

Abstract

This article is devoted to the maximisation of HARA utilities of L{\'e}vy switching process on finite time interval via dual method. We give the description of all f-divergence minimal martingale measures in initially enlarged filtration, the expression of their Radon-Nikodym densities involving Hellinger and Kulback-Leibler processes, the expressions of the optimal strategies in progressively enlarged filtration for the maximisation of HARA utilities as well as the values of the corresponding maximal expected utilities. The example of Brownian switching model is presented to give the financial interpretation of the results.