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A Multi-Marginal C-Convex Duality Theorem for Martingale Optimal Transport

Julian Sester

Abstract

A convex duality result for martingale optimal transport problems with two marginals was established in Beiglböck et al. (2013). In this paper we provide a generalization of this result to the multi-period setting.

A Multi-Marginal C-Convex Duality Theorem for Martingale Optimal Transport

Abstract

A convex duality result for martingale optimal transport problems with two marginals was established in Beiglböck et al. (2013). In this paper we provide a generalization of this result to the multi-period setting.
Paper Structure (5 sections, 2 theorems, 19 equations)

This paper contains 5 sections, 2 theorems, 19 equations.

Table of Contents

  1. Introduction
  2. The one-period convex duality result
  3. Main result
  4. Discussion of Proposition \ref{['prop_dual']} and relation to numerics
  5. Proof of Proposition \ref{['prop_dual']}

Key Result

Proposition 1.2

Let $c:\mathbb{R}^2 \rightarrow (-\infty,\infty]$ be lower semi-continuous and $c(x,y) \geq -K(1+|x|+|y|)$ for all $x,y \in \mathbb{R}$ and some $K \in \mathbb{R}$. Additionally assume there exists some probability measure $\mathbb{Q}' \in \mathcal{M}(\mu_1,\mu_2)$ such that $\mathbb{E}_\mathbb{Q}'[

Theorems & Definitions (4)

  • Definition 1.1: Convex Biconjugate
  • Proposition 1.2: beiglbock2013model, Proposition 4.4
  • Proposition 2.1
  • Remark 2.2