Utility Maximisation for Exponential Levy Models with option and information processes

TL;DR

This paper addresses utility maximisation in exponential Levy models with correlated assets, incorporating options and information processes, providing explicit formulas under certain Levy process assumptions.

Contribution

It introduces explicit expressions for information processes in utility maximisation problems involving correlated Levy models and options, extending classical models to include jumps and illiquid assets.

Findings

Derived formulas for information processes in Levy models

Applied results to Black-Scholes models with correlation and jumps

Extended utility maximisation framework to include illiquid assets

Abstract

We consider expected utility maximisation problem for exponential Levy models and HARA utilities in presence of illiquid asset in portfolio. This illiquid asset is modelled by an option of European type on another risky asset which is correlated with the first one. Under some hypothesis on Levy processes, we give the expressions of information processes figured in maximum utility formula. As applications, we consider Black-Scholes models with correlated Brownian Motions, and also Black-Scholes models with jump part represented by Poisson process.