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Exploring Optimisation Strategies Under Jump-Diffusion Dynamics

Author

Listed:
  • Luca Di Persio

    (Department of Computer Science, University of Verona, 37134 Verona, Italy)

  • Nicola Fraccarolo

    (Department of Mathematics, University of Trento, 38123 Trento, Italy)

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.

Suggested Citation

  • Luca Di Persio & Nicola Fraccarolo, 2025. "Exploring Optimisation Strategies Under Jump-Diffusion Dynamics," Mathematics, MDPI, vol. 13(3), pages 1-16, February.
    • Handle: RePEc:gam:jmathe:v:13:y:2025:i:3:p:535-:d:1584785
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