The Fundamental Theorem of Asset Pricing Without Probabilistic Prior Assumptions
19 Pages Posted: 24 Jul 2011
Date Written: July 22, 2011
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
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