论文标题
SPDE的奇异扰动和渐近扩展，并应用于期限结构模型
Singular perturbations and asymptotic expansions for SPDEs with an application to term structure models
论文作者
论文摘要
我们研究了温和解决方案对线性随机演化方程的依赖性对由维纳尔噪声驱动的希尔伯特空间的依赖性，而漂移的一部分是$ a+\ varepsilon g $的线性部分，对参数$ \ varepsilon $。特别是，我们研究了这些解决方案的$ \ varepsilon $以及其功能的限制和渐近扩展，为$ \ varepsilon \ to 0 $，其余部分可以很好地控制。然后将这些收敛性和串联扩展结果应用于数学金融的Musiela SPDE的抛物线扰动，以模拟远期速率的动力学。
We study the dependence of mild solutions to linear stochastic evolution equations on Hilbert space driven by Wiener noise, with drift having linear part of the type $A+\varepsilon G$, on the parameter $\varepsilon$. In particular, we study the limit and the asymptotic expansions in powers of $\varepsilon$ of these solutions, as well as of functionals thereof, as $\varepsilon \to 0$, with good control on the remainder. These convergence and series expansion results are then applied to a parabolic perturbation of the Musiela SPDE of mathematical finance modeling the dynamics of forward rates.
