DUAL FORMULATION OF SECOND ORDER TARGET PROBLEMS

• 成果类型: Article
• 署名作者: Soner, H. Mete; Touzi, Nizar; Zhang, Jianfeng
• 署名单位: Swiss Federal Institutes of Technology Domain; ETH Zurich; Swiss Finance Institute (SFI); Institut Polytechnique de Paris; Ecole Polytechnique; University of Southern California
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/12-AAP844
• 发表日期: 2013
• 页码: 308-347
• 关键词: STOCHASTIC DIFFERENTIAL-EQUATIONS; gamma-constraints; Contingent claims; THEOREM

摘要

This paper provides a new formulation of second order stochastic target problems introduced in [SIAM J. Control Optim. 48 (2009) 2344-2365] by modifying the reference probability so as to allow for different scales. This new ingredient enables us to prove a dual formulation of the target problem as the supremum of the solutions of standard backward stochastic differential equations. In particular, in the Markov case, the dual problem is known to be connected to a fully nonlinear, parabolic partial differential equation and this connection can be viewed as a stochastic representation for all nonlinear, scalar, second order, parabolic equations with a convex Hessian dependence.