Maximizing the probability of a perfect hedge

• 成果类型: Article
• 署名作者: Spivak, G; Cvitanic, J
• 署名单位: Columbia University
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• 发表日期: 1999
• 页码: 1303-1328
• 关键词: OPTIMAL CONSUMPTION; PORTFOLIO POLICIES; investor

摘要

In the framework of continuous-time, Ito processes models for financial markets, we study the problem of maximizing the probability of an agent's wealth at time T being no less than the value C of a contingent claim with expiration time T. The solution to the problem has been known in the context of complete markets and recently also for incomplete markets; we rederive the complete markets solution using a powerful and simple duality method, developed in utility maximization literature. We then show how to modify this approach to solve the problem in a market with partial information, the one in which we have only a prior distribution on the vector of return rates of the risky assets. Finally, the same problem is solved in markets in which the wealth process of the agent has a nonlinear drift. These include the case of different borrowing and lending rates, as well as large investor models. We also provide a number of explicitly solved examples.