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On perpetual American options in a multidimensional Black-Scholes model
Andrzej Rozkosz · 2019-01-02 · via math.PR updates on arXiv.org

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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