Minimax theorems for American options in incomplete markets without time-consistency
Probability
2017-08-30 v1 Mathematical Finance
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.
Keywords
Cite
@article{arxiv.1708.08904,
title = {Minimax theorems for American options in incomplete markets without time-consistency},
author = {Denis Belomestny and Volker Kraetschmer},
journal= {arXiv preprint arXiv:1708.08904},
year = {2017}
}