American options in a non-linear incomplete market model with default

Miryana Grigorova, Marie-Claire Quenez and Agnès Sulem

Stochastic Processes and their Applications, 2021, vol. 142, issue C, 479-512

Abstract: We study the superhedging problem for American options with completely irregular payoffs in a non-linear and incomplete market model with default. We give a dual representation of the seller’s (superhedging) price in terms of the value of a non-linear mixed control/stopping problem, involving a suitable set of equivalent probability measures. We characterize the seller’s price process as the minimal supersolution of two types of reflected BSDEs: a constrained one and an optional one. Under some regularity assumptions on the pay-off, we show a duality result for the buyer’s price in terms of the value of a non-linear control/stopping game problem.

Keywords: American options; Incomplete markets; Non-linear pricing; Constrained reflected BSDE; Irregular pay-off process; Non-linear optional decomposition (search for similar items in EconPapers)
Date: 2021
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Citations: View citations in EconPapers (1)

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DOI: 10.1016/j.spa.2021.09.004

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