Existence of a fundamental solution of partial differential equations associated to Asian options. (December 2021) - Anceschi, Francesca; Muzzioli, Silvia; Polidoro, Sergio
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.