Utility Maximization and Indifference Value under Risk and Information Constraints for a Market with a Change Point

TL;DR

This paper addresses an expected utility maximization problem in a financial market with a change point, incorporating information constraints and deriving optimal strategies and indifference values under various filtrations.

Contribution

It provides a solution to the utility maximization problem with market change points and information constraints, including explicit formulas for optimal wealth and indifference values.

Findings

Derived optimal terminal wealth depending on information flow.

Calculated utility indifference value for specific utility and risk measure.

Extended martingale representation results to enlarged filtrations.

Abstract

In this article we consider an optimization problem of expected utility maximization of continuous-time trading in a financial market. This trading is constrained by a benchmark for a utility-based shortfall risk measure. The market consists of one asset whose price process is modeled by a Geometric Brownian motion where the market parameters change at a random time. The information flow is modeled by initially and progressively enlarged filtrations which represent the knowledge about the price process, the Brownian motion and the random time. We solve the maximization problem and give the optimal terminal wealth depending on these different filtrations for general utility functions by using martingale representation results for the corresponding filtration. Moreover, for a special utility function and risk measure we calculate the utility indifference value which measures the gain of further information for the investor.