Finance Without Probabilistic Prior Assumptions

2011/07/06 by Frank Riedel, Riedel, Frank
Decision Sciences · Economics, Econometrics and Finance · #Economic theories and models #FOS: Economics and business #General Finance (q-fin.GN) #Risk and Portfolio Optimization #Stochastic processes and financial applications

paper · pdf · doi:10.48550/arxiv.1107.1078

openalex publication_date 2011/07/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Citations

• Financial markets with volatility uncertainty

Related

• Pricing without martingale measure
• Robust Fundamental Theorem for Continuous Processes
• Pricing without no-arbitrage condition in discrete time
• Finitely additive probabilities and the Fundamental Theorem of Asset Pricing
• Towards a probability-free theory of continuous martingales