Variance-optimal hedging for processes with stationary independent increments

• 成果类型: Article
• 署名作者: Hubalek, Friedrich; Kallsen, Jan; Krawczyk, Leszek
• 署名单位: Aarhus University; Technical University of Munich
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/105051606000000178
• 发表日期: 2006
• 页码: 853-885
• 关键词: utility maximization; incomplete markets; Optimal investment; DECOMPOSITION; martingale

摘要

We determine the variance-optimal hedge when the logarithm of the underlying price follows a process with stationary independent increments in discrete or continuous time. Although the general solution to this problem is known as back-ward recursion or backward stochastic differential equation, we show that for this class of processes the optimal endowment and strategy can be expressed more explicitly. The corresponding formula-,; involve the moment, respectively, cumulant generating function of the underlying process and a Laplace- or Fourier-type representation of the contingent claim. An example illustrates that our formulas are fast and easy to evaluate numerically.