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Duality methods in stochastic optimal control

Peter Bank, Filippo de Feo

Abstract

We prove two duality descriptions of the value function for a generic stochastic optimal problem. These descriptions also hold when the diffusion is controlled, a case left open by the literature so far.

Duality methods in stochastic optimal control

Abstract

We prove two duality descriptions of the value function for a generic stochastic optimal problem. These descriptions also hold when the diffusion is controlled, a case left open by the literature so far.
Paper Structure (5 sections, 2 theorems, 20 equations)

This paper contains 5 sections, 2 theorems, 20 equations.

Table of Contents

  1. Introduction
  2. Setting of the problem
  3. Classical solutions
  4. Non-smooth case
  5. Acknowledgments.

Key Result

Theorem 3.2

Assume that $V \in C^{1,2}((0, T) \times \mathbb{R}^d) \cap C((0, T] \times \mathbb{R}^d)$ is a classical solution of HJB. Then where $\mathcal{H}:=\{h \in C^{1,2}( (0,T)\times \mathbb R^d): h(x,T)=g(x) \}$ and

Theorems & Definitions (7)

  • Definition 3.1
  • Theorem 3.2
  • proof
  • Remark 3.3
  • Remark 4.2
  • Theorem 4.3
  • proof