2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/103135In this paper we provide an extensive classification of one and two dimensional diffusion processes which admit an exact solution to the Kolmogorov (and hence Black-Scholes) equation (in terms of hypergeometric functions). By identifying the one-dimensional solvable processes with the class of integrable superpotentials introduced recently in supersymmetric quantum mechanics, we obtain new analytical solutions. For two-dimensional processes, more precisely stochastic volatility models, the classification is achieved for a specific class called gauge-free models including the Heston model, the 3/2-model and the geometric Brownian model.Other Condensed Mattertext