Small time path behavior of double stochastic integrals and applications to stochastic control

• 成果类型: Article
• 署名作者: Cheridito, P; Soner, HM; Touzi, N
• 署名单位: Princeton University; Koc University; Institut Polytechnique de Paris; ENSAE Paris
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/105051605000000557
• 发表日期: 2005
• 页码: 2472-2495
• 关键词: target problems

摘要

We study the small time path behavior of double stochastic integrals of othe form f(0)(t)(f(0)(r) b(u) dW(u))(T) dW(r), where W is ad-dimensional Brownian motion and b is an integrable progressively measurable stochastic process taking values in the set of d x d-matrices. We prove a law of the iterated logarithm that holds for all bounded progressively measurable b and give additional results under continuity assumptions on b. As an application, we discuss a stochastic control problem that arises in the study of the super-replication of a contingent claim under gamma constraints.