Mathematics – Probability
Scientific paper
2011-03-02
Mathematics
Probability
To appear in the Proceedings of the American Mathematical Society; Key words: Perron's method, viscosity solutions, non-smooth
Scientific paper
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
Bayraktar Erhan
Sirbu Mihai
No associations
LandOfFree
Stochatic Perron's method and verification without smoothness using viscosity comparison: the linear case does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Stochatic Perron's method and verification without smoothness using viscosity comparison: the linear case, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Stochatic Perron's method and verification without smoothness using viscosity comparison: the linear case will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-587924