Existence of a Fundamental Solution of Partial Differential Equations associated to Asian Options

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.

34 pages

References in corpus (1)

• On stochastic Langevin and Fokker-Planck equations: the two-dimensional case

Cited by in corpus (2)

• Global $L_p$ estimates for kinetic Kolmogorov-Fokker-Planck equations in nondivergence form
• $L_1$ and $L_{\infty }$ stability of transition densities of perturbed diffusions