Finance Without Probabilistic Prior Assumptions
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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- Epstein, Larry G. & Ji, Shaolin, 2014.
"Ambiguous volatility, possibility and utility in continuous time,"
Journal of Mathematical Economics,
Elsevier, vol. 50(C), pages 269-282.
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