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

• DOI: 10.1016/j.nonrwa.2021.103373
• Publication Date: 2021-06-11T00:28:43Z
• Authors: Francesca Anceschi; Silvia Muzzioli; Sergio Polidoro
• Keywords: Limiting; Operator (biology); Expression (computer science)

34 pages<br/>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.<br/>