Wednesday, October 30, 2019 - 14:00 in V3-201
Minimax theorems for American options without time-consistency
A talk in the Bielefeld Stochastic Afternoon series by
Volker Krätschmer from University of Duisburg-Essen
| Abstract: |
In the talk we shall present sufficient conditions guaranteeing validity of the well-known minimax theorem for the lower Snell envelope. Such minimax results play an important role in the characterisation of arbitrage-free prices of American contingent claims in incomplete markets. Our conditions do not rely on the notions of stability under pasting or time-consistency and reveal some unexpected connection between the minimax result and path properties of the corresponding density process. We shall exemplify our general results in the case of families of measures corresponding to diffusion exponential martingales with some substantial refinements obtained recently. At the end of the talk we shall discuss how to extend the minimax results to the model free situation where no reference probability measure is given in advance. The talk is based on a joint work with Denis Belomestny, Tobias Hübner and Sascha Nolte.
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