What question did this study set out to answer?

The goal is to maximize portfolio utility by incorporating jump signals alongside traditional Brownian motion.

April 16, 2026Open Access

Portfolio Exponential Utility Maximization with Jump Signals

Key Points

The goal is to maximize portfolio utility by incorporating jump signals alongside traditional Brownian motion.
Developed a framework for portfolio utility maximization using jump signals in asset prices.
Expressed the portfolio as semi-martingale processes applying martingale optimality principles.
Derived a backward stochastic differential equation (BSDE) with jumps to find optimal strategies and values.
Proved the existence of a solution for the BSDE and conducted numerical experiments.
Demonstrated improvements in utility maximization when jump signals are incorporated into strategies.
Quantified the gain in utility resulting from utilizing information from jump signals.

Abstract

In this paper, we study the portfolio utility maximization in the case where the risky asset is driven by a Brownian motion and an independent homogeneous Poisson measure, with strategies that may include jump signals. This means that the allowed strategies are no longer predictable but also include the information given by a process driven by the Poisson measure. Using the results of Bank and Körber 1, we first express the considered portfolio as semi-martingale processes. We then present the martingale optimality principle for the exponential utility maximization. This allows to derive an original BSDE with jumps and to express the optimal value and an optimal strategy using the solution to this original BSDE. We then prove existence of a solution to the considered BSDE. We finally present some numerical experiments to quantify the gain of utility given by the information from the jump signals.

Portfolio Exponential Utility Maximization with Jump Signals

Key Points

Abstract

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