Article Dans Une Revue Journal of Advances in Mathematics and Computer Science  Année : 2025

Combinatorial Approximation Method for the Fractional Stochastic Hamilton–Jacobi–Bellman Equation

Résumé

We introduce a combinatorial method for approximating the solution of a very complicated nonlinear fractional stochastic partial differential equation (SPDE) which appears in optimal stochastic control. We extend our previous research on the fractional SABR (Stochastic Alpha Beta Rho) model where we could derive only an approximation of the shadow price without the explicit formulas for utility function maximization. We aim to solve the equation by integrating combinatorial techniques with fractional calculus to address the system’s inherent randomness and memory effects. The ensuing approximation framework provides analytical tractability for the fractional stochastic Hamilton–Jacobi–Bellman equation and shows promise of applicability to fields like quantitative finance, physics, and engineering, where sound decisionmaking under uncertainty is critical.

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Dates et versions

hal-05223238 , version 1 (26-08-2025)

Identifiants

  • HAL Id : hal-05223238 , version 1

Citer

Abel Zongo, Finyori Fayama, Raogo Frank Emile Er Jumeau Kabore, S. Pierre Clovis Nitiema. Combinatorial Approximation Method for the Fractional Stochastic Hamilton–Jacobi–Bellman Equation. Journal of Advances in Mathematics and Computer Science , 2025, 40 (9), pp.24-35. ⟨hal-05223238⟩
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