Robust martingale selection problem and its connections to the no-arbitrage theory

TL;DR

This paper explores the robust martingale selection problem, establishing conditions for its solvability and linking it to no-arbitrage theory across various market models with constraints.

Contribution

It extends the martingale selection problem to a robust setting and connects it to fundamental no-arbitrage results in diverse market scenarios.

Findings

Derived solvability conditions for the robust martingale selection problem.

Established versions of the Fundamental Theorem of Asset Pricing in multiple market models.

Connected the martingale selection problem to no-arbitrage principles under trading constraints.

Abstract

We analyze the martingale selection problem of Rokhlin (2006) in a pointwise (robust) setting. We derive conditions for solvability of this problem and show how it is related to the classical no-arbitrage deliberations. We obtain versions of the Fundamental Theorem of Asset Pricing in examples spanning frictionless markets, models with proportional transaction costs and also models for illiquid markets. In all these examples, we also incorporate trading constraints.