Maturity randomization for stochastic control problems

• 成果类型: Article
• 署名作者: Bouchard, B; El Karoui, N; Touzi, N
• 署名单位: Universite Paris Cite; Sorbonne Universite; Institut Polytechnique de Paris; ENSAE Paris; Institut Polytechnique de Paris; Ecole Polytechnique; Universite PSL; Universite Paris-Dauphine
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/105051605000000593
• 发表日期: 2005
• 页码: 2575-2605
• 关键词: PORTFOLIO CONSTRAINTS; super-replication; volatility

摘要

We study a maturity randomization technique for approximating optimal control problems. The algorithm is based on a sequence of control problems with random terminal horizon which converges to the original one. This is a generalization of the so-called Canadization procedure suggested by Carr [Review of Financial Studies II (1998) 597-626] for the fast computation of American put option prices. In addition to the original application of this technique to optimal stopping problems, we provide an application to another problem in finance, namely the super-replication problem under stochastic volatility, and we show that the approximating value functions can be computed explicitly.