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

Patrick Cheridito, H. Mete Soner, Nizar Touzi

Research output: Contribution to journalArticle

11 Scopus citations

Abstract

We study the small time path behavior of double stochastic integrals of the form f 0 t (f 0 r b(u) dW(u)) T dW(r), where W is a d-dimensional Brownian motion and b is an integrable progressively measurable stochastic process taking values in the set of d × 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.

Original languageEnglish (US)
Pages (from-to)2472-2495
Number of pages24
JournalAnnals of Applied Probability
Volume15
Issue number4
DOIs
StatePublished - Nov 1 2005
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

Keywords

  • Double stochastic integrals
  • Hedging under gamma constraints
  • Law of the iterated logarithm
  • Stochastic con-trol

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