Finance Without Probabilistic Prior Assumptions
Posted: 20 Mar 2012
Date Written: July 11, 2011
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
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