Variational Inequalities in Hilbert Spaces with Measures and Optimal Stopping Problems

Variational Inequalities in Hilbert Spaces with Measures and Optimal Stopping Problems
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希尔伯特空间中的变分不等式及其测度和最优停止问题

DOI：
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发表时间：
2006
期刊：
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通讯作者：
Carlo Marinelli
Carlo Marinelli
中科院分区：
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文献类型：
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作者：
V. Barbu;Carlo Marinelli

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摘要 我们研究了加权L2空间中抛物型变分不等式关于过渡半群的过度测度的存在性理论。我们将有限维和无限维扩散的最优停止问题的值函数刻画为此类变分不等式的广义解。加权L2设置允许我们覆盖一些奇异情况，例如具有退化扩散系数的随机方程的最优停止。作为理论的一个应用，我们考虑了美式未定权益的定价。其中，我们处理具有随机波动性和路径依赖收益的资产的情况。
Abstract We study the existence theory for parabolic variational inequalities in weighted L2 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 L2 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.