Existence of a fundamental solution of partial differential equations associated to Asian options. (December 2021)

• Record Type: Journal Article
• Authors: Anceschi, Francesca; Muzzioli, Silvia; Polidoro, Sergio
• Is Part Of: Nonlinear analysis. Volume 62(2021)
• Publication Date: 2021-12
• Subjects: Partial differential equations -- Option pricing -- Kolmogorov operator; Nonlinear functional analysis -- Periodicals; Analyse fonctionnelle non linéaire -- Périodiques; Nonlinear functional analysis; Periodicals; 515.7248
• DOI: 10.1016/j.nonrwa.2021.103373
• Languages: English
• ISSNs: 1468-1218

Abstract

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.