MIMICKING AN ITO PROCESS BY A SOLUTION OF A STOCHASTIC DIFFERENTIAL EQUATION
MIMICKING AN ITO PROCESS BY A SOLUTION OF A STOCHASTIC DIFFERENTIAL EQUATION
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DOI：
10.1214/12-aap881
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发表时间：
2013-08-01
影响因子：
1.8
通讯作者：
Shreve, Steven
中科院分区：
文献类型：
--
作者：
Brunick, Gerard;Shreve, Steven
给定一个多维Ito过程的漂移和扩散项是适应过程，我们构造一个弱解的随机微分方程，匹配的分布在每个固定的时间的Ito过程。此外，我们展示了如何匹配的分布在每个固定的时间的泛函的伊藤过程，包括运行的最大值和运行的平均值的一个组件的过程。这个结果的一个后果是，各种各样的外来衍生证券具有相同的价格时，标的资产的价格是由原来的伊藤过程或模拟过程，解决了随机微分方程。
Given a multi-dimensional Ito process whose drift and diffusion terms are adapted processes, we construct a weak solution to a stochastic differential equation that matches the distribution of the Ito process at each fixed time. Moreover, we show how to match the distributions at each fixed time of functionals of the Ito process, including the running maximum and running average of one of the components of the process. A consequence of this result is that a wide variety of exotic derivative securities have the same prices when the underlying asset price is modeled by the original Ito process or the mimicking process that solves the stochastic differential equation.