The Fundamental Theorem of Asset Pricing Without Probabilistic Prior Assumptions

19 Pages Posted: 24 Jul 2011

See all articles by Frank Riedel

Frank Riedel

Bielefeld University - Center for Mathematical Economics

Date Written: July 22, 2011

Abstract

Motivated by recent discussions on Knightian uncertainty, we develop the fundamental theorem of asset pricing in a probability-free setup. The usual assumption of a prior probability is removed; a certain continuity property in the state variable is introduced instead. We show that one can still develop a meaningful and rich theory of asset pricing. The pricing functional given by an arbitrage-free market can be identified with a full support martingale measure (instead of equivalent martingale measure). We relate the no arbitrage theory to economic equilibrium by establishing a variant of the Harrison-Kreps-Theorem on viability and no arbitrage. Finally, we consider (super)hedging of contingent claims and embed it 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, The Fundamental Theorem of Asset Pricing Without Probabilistic Prior Assumptions (July 22, 2011). Available at SSRN: https://ssrn.com/abstract=1892706 or http://dx.doi.org/10.2139/ssrn.1892706

Frank Riedel (Contact Author)

Bielefeld University - Center for Mathematical Economics ( email )

Postfach 10 01 31
Bielefeld, D-33501
Germany

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