Finance Without Probabilistic Prior Assumptions

Posted: 20 Mar 2012

See all articles by Frank Riedel

Frank Riedel

Bielefeld University - Center for Mathematical Economics

Date Written: July 11, 2011

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.

Keywords: Probability-Free Finance, Fundamental Theorem of Asset Pricing, Full-Support Martingale Measure, Superhedging, Infinite-Dimensional Linear Programming

JEL Classification: G12, D53

Suggested Citation

Riedel, Frank, Finance Without Probabilistic Prior Assumptions (July 11, 2011). Institute of Mathematical Economics Working Paper No. 450, Available at SSRN: https://ssrn.com/abstract=2026209

Frank Riedel (Contact Author)

Bielefeld University - Center for Mathematical Economics ( email )

Postfach 10 01 31
Bielefeld, D-33501
Germany

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