Year: 2016
Type: article
Abstract: In this paper, a Banach space framework is introduced in order to deal with finite-dimensional path-dependent stochastic differential equations. A version of Kolmogorov backward equation is formulated and solved both in the space of $L^{p}$ paths and in the space of continuous paths using the associated stochastic differential equation, thus establishing a relation between path-dependent SDEs and PDEs in analogy with the classical case. Finally, it is shown how to establish a connection between such Kolmogorov equation and the analogue finite-dimensional equation that can be formulated in terms of the path-dependent derivatives recently introduced by Dupire, Cont and Fournié.
Source: The Annals of Probability
DOI: 10.1214/15-aop1031
Authors: Franco Flandoli, Giovanni Zanco
Institution: University of Pisa
Language: English
Subfield: Finance
Domain: Social Sciences
Open Access status: bronze
OpenAlex ID: W1574346102