Finance Without Probabilistic Prior Assumptions

TL;DR

This paper establishes a probability-free framework for asset pricing in infinite dimensions, replacing prior probabilities with continuity properties, and connects superhedging to linear programming.

Contribution

It introduces a novel probability-free approach to the fundamental theorem of asset pricing in infinite-dimensional spaces, replacing prior assumptions with continuity conditions.

Findings

Probabilities emerge endogenously as full support martingale measures

A variant of Harrison-Kreps-Theorem on viability and no arbitrage is proven

Superhedging is formulated as an infinite-dimensional linear programming problem

Abstract

We develop the fundamental theorem of asset pricing in a probability-free infinite-dimensional setup. We replace the usual assumption of a prior probability by a certain continuity property in the state variable. Probabilities enter then endogenously as full support martingale measures (instead of equivalent martingale measures). A variant of the Harrison-Kreps-Theorem on viability and no arbitrage is shown. Finally, we show how to embed the superhedging problem in a classical infinite-dimensional linear programming problem.