MONOTONICITY OF THE VALUE FUNCTION FOR A TWO-DIMENSIONAL OPTIMAL STOPPING PROBLEM

• 成果类型: Article
• 署名作者: Assing, Sigurd; Jacka, Saul; Ocejo, Adriana
• 署名单位: University of Warwick
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/13-AAP956
• 发表日期: 2014
• 页码: 1554-1584
• 关键词: american; options

摘要

We consider a pair (X, Y) of stochastic processes satisfying the equation dX = a(X)Y dB driven by a Brownian motion and study the monotonicity and continuity in y of the value function nu(x, y) = sup(tau) E-x,E-y[e(-q tau)g(X-tau)], where the supremum is taken over stopping times with respect to the filtration generated by (X, Y). Our results can successfully be applied to pricing American options where X is the discounted price of an asset while Y is given by a stochastic volatility model such as those proposed by Heston or Hull and White. The main method of proof is based on time-change and coupling.