Forward Backward SDEs Systems for Utility Maximization in Jump Diffusion Models

Paper: arXiv 2302.08253

Authors: Marina Santacroce, Paola Siri, Barbara Trivellato

Abstract

We consider the classical problem of maximizing the expected utility of terminal net wealth with a final random liability in a simple jump-diffusion model. In the spirit of Horst et al. (2014) and Santacroce-Trivellato (2014), under suitable conditions the optimal strategy is expressed in implicit form in terms of a forward backward system of equations. Some explicit results are presented for the pure jump model and for exponential utilities.

Complexity vs Empirical Score

• Math Complexity: 8.5/10
• Empirical Rigor: 1.5/10
• Quadrant: Lab Rats — theoretically deep, empirically untested

Why this score: The paper presents high mathematical rigor using forward-backward stochastic differential equations (FBSDEs) and jump-diffusion models for utility maximization. However, it is purely theoretical with no empirical backtesting, empirical validation, or real-world market data implementations.

Research Flowchart

  flowchart TD
    A[Goal: Maximize Expected Utility of Terminal Wealth with Random Liability] --> B[Inputs: Jump-Diffusion Model & Exponential Utility Functions]
    B --> C[Formulate Stochastic Control Problem with Liabilities]
    C --> D[Derive Value Function & Apply Dynamic Programming]
    D --> E[Solve via Forward-Backward SDE System]
    E --> F[Outcomes: Implicit Optimal Strategy & Explicit Pure Jump Solutions]