Stochatic Perron's method and verification without smoothness using viscosity comparison: the linear case
Year: 2011
Type: preprint
Abstract: We introduce a probabilistic version of the classical Perron's method to construct viscosity solutions to linear parabolic equations associated to stochastic differential equations. Using this method, we construct easily two viscosity (sub and super) solutions that squeeze in between the expected payoff. If a comparison result holds true, then there exists a unique viscosity solution which is a martingale along the solutions of the stochastic differential equation. The unique viscosity solution is actually equal to the expected payoff. This amounts to a verification result (Ito's Lemma) for non-smooth viscosity solutions of the linear parabolic equation. This is the first step in a larger program to prove verification for viscosity solutions and the Dynamic Programming Principle for stochastic control problems and games
Source: arXiv (Cornell University)
Authors: Bayraktar, Erhan, Sirbu, Mihai
Institutions: University of Michigan, The University of Texas at Austin
Language: English
Subfield: Finance
Domain: Social Sciences
Open Access status: green
Funder: National Science Foundation
OpenAlex ID: W2952669429