Finance Without Probabilistic Prior Assumptions
General Finance
2011-07-07 v1
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.
Keywords
Cite
@article{arxiv.1107.1078,
title = {Finance Without Probabilistic Prior Assumptions},
author = {Frank Riedel},
journal= {arXiv preprint arXiv:1107.1078},
year = {2011}
}