Finance Without Probabilistic Prior Assumptions

Frank Riedel

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arXiv · 1107.1078

Finance Without Probabilistic Prior Assumptions

Frank Riedel

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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.

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Frank Riedel. 2011-07-06. Finance Without Probabilistic Prior Assumptions. https://arxiv.org/abs/1107.1078

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