MIMICKING AN ITO PROCESS BY A SOLUTION OF A STOCHASTIC DIFFERENTIAL EQUATION

• 成果类型: Article
• 署名作者: Brunick, Gerard; Shreve, Steven
• 署名单位: University of California System; University of California Santa Barbara; Carnegie Mellon University
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/12-AAP881
• 发表日期: 2013
• 页码: 1584-1628
• 关键词: time-homogeneous diffusions; continuous coefficients; marginal distributions; martingales; LAW

摘要

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.