Fractional Stochastic Optimal Control: Malliavin Calculus and Risk-Sensitive Maximum Principle

Bibliographic information

Publication date

2026

Language

Anglais

ISBN

978-9969-677-69-0

Pages

100

Format

16 × 24 cm

Subject Area

Mathématiques et Informatique

Abstract

This book develops stochastic optimal control for systems driven by standard and fractional Brownian motions using Malliavin calculus and Pontryagin’s maximum principle. It first introduces Malliavin derivatives, duality and integration-by-parts formulas, fractional Brownian motion, Russo–Vallois integration, and the Doss–Sussmann transformation. It then derives necessary and sufficient optimality conditions for backward doubly stochastic differential equations under risk-neutral criteria. A third chapter presents fractional Girsanov transformations together with existence and uniqueness results for fractional backward stochastic differential equations. The final chapter establishes risk-sensitive necessary and sufficient maximum principles, transforms the adjoint equation, and applies the framework to a linear-quadratic financial control problem. An explicit Riccati-equation solution completes the application, illustrating how fractional stochastic methods support optimization under uncertainty and long-range dependence effects.

Authors and contributors

Suggested citation

BOUAZIZ Tayeb. Fractional Stochastic Optimal Control: Malliavin Calculus and Risk-Sensitive Maximum Principle. SARAHMED Éditions, 2026. ISBN : 978-9969-677-69-0