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arXiv · 1901.00308

On perpetual American options in a multidimensional Black-Scholes model

Andrzej Rozkosz
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Abstract

We consider the problem of pricing perpetual American options written on dividend-paying assets whose price dynamics follow a multidimensional Black and Scholes model. For convex Lipschitz continuous reward functions, we give a probabilistic characterization of the fair price in terms of a reflected BSDE, and an analytical one in terms of an obstacle problem. We also provide the early exercise premium formula.

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Andrzej Rozkosz. 2019-01-02. On perpetual American options in a multidimensional Black-Scholes model. https://doi.org/10.1080/17442508.2021.1993444

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