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Minimax theorems for American options without time-consistency

Denis Belomestny (), Tobias Hübner (), Volker Krätschmer () and Sascha Nolte ()
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Denis Belomestny: University of Duisburg–Essen
Tobias Hübner: University of Duisburg–Essen
Volker Krätschmer: University of Duisburg–Essen
Sascha Nolte: University of Duisburg–Essen

Finance and Stochastics, 2019, vol. 23, issue 1, 209-238

Abstract: Abstract In this paper, we give sufficient conditions guaranteeing the 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 process of densities. We exemplify our general results in the case of families of measures corresponding to diffusion exponential martingales.

Keywords: Minimax; Lower Snell envelope; Time-consistency; Nearly sub-Gaussian random fields; Metric entropies; Simons’ lemma; 60G40; 90C47; 91G20; 60G17 (search for similar items in EconPapers)
JEL-codes: C73 G12 D81 (search for similar items in EconPapers)
Date: 2019
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