Finance without probabilistic prior assumptions - Frank Riedel (Bielefeld University, Institute of Mathematical Economics (IMW), 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: G12; D53; 330; Probability-Free Finance; Fundamental Theorem of Asset Pricing; Full-Support Martingale Measure; Superhedging; Infinite-Dimensional Linear Programming; Finanzanalyse; Martingale; Hedging; Theorie