Exploring Optimisation Strategies Under Jump-Diffusion Dynamics

Luca Di Persio and Nicola Fraccarolo ()
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Luca Di Persio: Department of Computer Science, University of Verona, 37134 Verona, Italy
Nicola Fraccarolo: Department of Mathematics, University of Trento, 38123 Trento, Italy

Mathematics, 2025, vol. 13, issue 3, 1-16

Abstract: This paper addresses the portfolio optimisation problem within the jump-diffusion stochastic differential equations (SDEs) framework. We begin by recalling a fundamental theoretical result concerning the existence of solutions to the Black–Scholes–Merton partial differential equation (PDE), which serves as the cornerstone for subsequent analysis. Then, we explore a range of financial applications, spanning scenarios characterised by the absence of jumps, the presence of jumps following a log-normal distribution, and jumps following a distribution of greater generality. Additionally, we delve into optimising more complex portfolios composed of multiple risky assets alongside a risk-free asset, shedding new light on optimal allocation strategies in these settings. Our investigation yields novel insights and potentially groundbreaking results, offering fresh perspectives on portfolio management strategies under jump-diffusion dynamics.

Keywords: portfolio optimisation; merton problem; optimal allocation strategies; jump-diffusion stochastic differential equations; Lévy processes; verification theorem (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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