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Anceschi, Francesca; Muzzioli, Silvia; Polidoro, Sergio, (2021)  - Existence of a fundamental solution of partial differential equations associated to Asian options  - NONLINEAR ANALYSIS: REAL WORLD APPLICATIONS, Articolo su rivista - Articolo in rivista (262) (, , ) - pagg. 1 - 29

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.