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arXiv · 2007.09037

Existence of a Fundamental Solution of Partial Differential Equations associated to Asian Options

Francesca Anceschi·Silvia Muzzioli·Sergio Polidoro
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Abstract

We prove the existence and uniqueness of the fundamental solution for Kolmogorov operators associated to some stochastic processes, that arise in the Black & Scholes setting for the pricing problem relevant to path dependent options. We improve previous results in that we provide a closed form expression for the solution of the Cauchy problem under weak regularity assumptions on the coefficients of the differential operator. Our method is based on a limiting procedure, whose convergence relies on some barrier arguments and uniform a priori estimates recently discovered.

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Francesca Anceschi, Silvia Muzzioli, Sergio Polidoro. 2020-07-17. Existence of a Fundamental Solution of Partial Differential Equations associated to Asian Options. https://doi.org/10.1016/j.nonrwa.2021.103373

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