Variational Inequalities in Hilbert Spaces with Measures and Optimal Stopping Problems
Journal Article
·
· Applied Mathematics and Optimization
- University Al. I. Cuza (Romania)
- Universitaet Bonn, Institut fuer Angewandte Mathematik (Germany)
We study the existence theory for parabolic variational inequalities in weighted L{sup 2} spaces with respect to excessive measures associated with a transition semigroup. We characterize the value function of optimal stopping problems for finite and infinite dimensional diffusions as a generalized solution of such a variational inequality. The weighted L{sup 2} setting allows us to cover some singular cases, such as optimal stopping for stochastic equations with degenerate diffusion coefficient. As an application of the theory, we consider the pricing of American-style contingent claims. Among others, we treat the cases of assets with stochastic volatility and with path-dependent payoffs.
- OSTI ID:
- 21064174
- Journal Information:
- Applied Mathematics and Optimization, Journal Name: Applied Mathematics and Optimization Journal Issue: 2 Vol. 57; ISSN 0095-4616
- Country of Publication:
- United States
- Language:
- English
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