$F$-divergence minimal equivalent martingale measures and optimal portfolios for exponential Levy models with a change-point

TL;DR

This paper analyzes exponential Levy models with a change-point, deriving conditions for equivalent martingale measures and optimal portfolios, including explicit formulas for the Black-Scholes model with a change-point.

Contribution

It provides a comprehensive characterization of all equivalent martingale measures and derives optimal investment strategies in change-point exponential Levy models.

Findings

Characterization of all equivalent martingale measures for change-point models

Conditions for existence of f-divergence minimal measures

Explicit optimal strategies in Black-Scholes with change-point

Abstract

We study exponential Levy models with change-point which is a random variable, independent from initial Levy processes. On canonical space with initially enlarged filtration we describe all equivalent martingale measures for change-point model and we give the conditions for the existence of f-divergence minimal equivalent martingale measure. Using the connection between utility maximisation and $f$-divergence minimisation, we obtain a general formula for optimal strategy in change-point case for initially enlarged filtration and also for progressively enlarged filtration in the case of exponential utility. We illustrate our results considering the Black-Scholes model with change-point.