Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

New approach to optimal control of delayed stochastic Volterra integral equations

Roméo Kouassi Konan, Auguste Aman

Abstract

We address the optimal control of stochastic Volterra integral equations with delay through the lens of Hida-Malliavin calculus. We show that the corresponding adjoint processes satisfy an anticipated backward stochastic Volterra integral equation (ABSVIE), and, exploiting this structure, we establish both necessary and sufficient stochastic maximum principles. Our results provide a comprehensive and rigorous framework for characterizing optimal controls in delayed stochastic systems.

New approach to optimal control of delayed stochastic Volterra integral equations

Abstract

We address the optimal control of stochastic Volterra integral equations with delay through the lens of Hida-Malliavin calculus. We show that the corresponding adjoint processes satisfy an anticipated backward stochastic Volterra integral equation (ABSVIE), and, exploiting this structure, we establish both necessary and sufficient stochastic maximum principles. Our results provide a comprehensive and rigorous framework for characterizing optimal controls in delayed stochastic systems.

Paper Structure

This paper contains 5 sections, 6 theorems, 91 equations.

Table of Contents

  1. Introduction
  2. Formulation of problem
  3. Time-advanced BSVIE for adjoint equations
  4. Sufficient Maximum Principle
  5. A necessary maximum principle

Key Result

Proposition 2.1

(Generalized Clark--Ocone Formula Aase2000) For all $F \in L^2(\mathcal{F}_T, \mathbb{P})$, we have:

Theorems & Definitions (11)

  • Proposition 2.1
  • Proposition 2.2
  • proof
  • Theorem 2.1
  • Theorem 3.1
  • proof
  • Remark 3.2
  • Theorem 4.1
  • proof
  • Theorem 5.1: Necessary Maximum Principle
  • ...and 1 more