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.

Existence of a fundamental solution of partial differential equations associated to Asian options / Anceschi, Francesca; Muzzioli, Silvia; Polidoro, Sergio. - In: NONLINEAR ANALYSIS: REAL WORLD APPLICATIONS. - ISSN 1468-1218. - 62:(2021), pp. 1-29. [10.1016/j.nonrwa.2021.103373]

Existence of a fundamental solution of partial differential equations associated to Asian options

Muzzioli, Silvia
Membro del Collaboration Group
;
Polidoro, Sergio
Membro del Collaboration Group
2021

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.
11-giu-2021
62
1
29
Existence of a fundamental solution of partial differential equations associated to Asian options / Anceschi, Francesca; Muzzioli, Silvia; Polidoro, Sergio. - In: NONLINEAR ANALYSIS: REAL WORLD APPLICATIONS. - ISSN 1468-1218. - 62:(2021), pp. 1-29. [10.1016/j.nonrwa.2021.103373]
Anceschi, Francesca; Muzzioli, Silvia; Polidoro, Sergio
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11380/1246756
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