The stochastic balance equation for the American option value function and its gradient

Malkhaz Shashiashvili

Stochastic Processes and their Applications, 2023, vol. 166, issue C

Abstract: In the paper we consider the problem of valuation and hedging of American options written on dividend-paying assets whose price dynamics follow a multidimensional diffusion model. We derive a stochastic balance equation for the American option value function and its gradient. We prove that the latter pair is the unique solution of the stochastic balance equation as a result of the uniqueness in the related adapted future-supremum problem. The latter problem has an attractive interpretation: the given adapted stochastic process can be adjusted by a martingale in such a manner, that the observer will gain the perfect foresight of the resulting future-supremum process via the Snell envelope of the given stochastic process.

Keywords: American option; Adapted future-supremum; Stochastic balance equation; Snell envelope (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1016/j.spa.2023.09.011

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