MEAN-VARIANCE HEDGING VIA STOCHASTIC CONTROL AND BSDES FOR GENERAL SEMIMARTINGALES

• 成果类型: Article
• 署名作者: Jeanblanc, Monique; Mania, Michael; Santacroce, Marina; Schweizer, Martin
• 署名单位: Universite Paris Saclay; Polytechnic University of Turin; Swiss Federal Institutes of Technology Domain; ETH Zurich; Swiss Finance Institute (SFI)
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/11-AAP835
• 发表日期: 2012
• 页码: 2388-2428
• 关键词: martingale measure

摘要

We solve the problem of mean-variance hedging for general semimartingale models via stochastic control methods. After proving that the value process of the associated stochastic control problem has a quadratic structure, we characterize its three coefficient processes as solutions of semimartingale backward stochastic differential equations and show how they can be used to describe the optimal trading strategy for each conditional mean-variance hedging problem. For comparison with the existing literature, we provide alternative equivalent versions of the BSDEs and present a number of simple examples.