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arXiv · 1708.08904

Minimax theorems for American options in incomplete markets without time-consistency

Denis Belomestny·Volker Kraetschmer
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Abstract

In this paper we give sufficient conditions guaranteeing the validity of the well-known minimax theorem for the lower Snell envelope with respect to a family of absolutely continuous probability measures. 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 the path properties of the corresponding density process.

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Denis Belomestny, Volker Kraetschmer. 2017-08-29. Minimax theorems for American options in incomplete markets without time-consistency. https://arxiv.org/abs/1708.08904

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