Variational Inequalities in Hilbert Spaces with Measures and Optimal Stopping Problems

Journal Article · Tue Apr 15 00:00:00 EDT 2008 · Applied Mathematics and Optimization

DOI:https://doi.org/10.1007/S00245-007-9021-X· OSTI ID:21064174

Barbu, Viorel ^[1]; Marinelli, Carlo ^[2]

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1. University Al. I. Cuza (Romania)
2. 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, Vol. 57, Issue 2; Other Information: DOI: 10.1007/s00245-007-9021-x; Copyright (c) 2008 Springer Science+Business Media, LLC; Country of input: International Atomic Energy Agency (IAEA); ISSN 0095-4616
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
DIFFUSION
EQUATIONS
FUNCTIONS
HILBERT SPACE
MATHEMATICAL SOLUTIONS
STOCHASTIC PROCESSES
VARIATIONAL METHODS