Variational inequalities in Hilbert spaces with measures and optimal stopping problems

Details Variational inequalities in Hilbert spaces with measures and optimal stopping problems Variational inequalities in Hilbert spaces with measures and optimal stopping problems

2006-08-15

arxiv.org/abs/math/0608379v2

Mathematics

Analysis of PDEs

To appear in Applied Mathematics and Optimization

Scientific paper

We study the existence theory for parabolic variational inequalities in weighted $L^2$ 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 $L^2$ 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.

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