Another example of duality between game-theoretic and measure-theoretic probability

TL;DR

This paper advances the understanding of superhedging duality by establishing the equivalence of game-theoretic and measure-theoretic expectations for certain functionals in a simplified setting, introducing a broader definition of game-theoretic probability.

Contribution

It provides a new proof of duality in a non-stochastic framework for a single security with continuous paths, using a broader definition of game-theoretic probability.

Findings

Game-theoretic and measure-theoretic expectations coincide for lower semicontinuous positive functionals.

Introduces a new broad definition of game-theoretic probability.

Progresses towards a non-stochastic superhedging duality theory.

Abstract

This paper makes a small step towards a non-stochastic version of superhedging duality relations in the case of one traded security with a continuous price path. Namely, we prove the coincidence of game-theoretic and measure-theoretic expectation for lower semicontinuous positive functionals. We consider a new broad definition of game-theoretic probability, leaving the older narrower definitions for future work.