@MISC{Riedel11financewithout, author = {Frank Riedel}, title = {Finance without Probabilistic Prior Assumptions}, year = {2011} }

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Abstract

This paper is dedicated to the students of the class “Advanced Topics in Finance ” at Bielefeld University in Summer 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.