Optimal investment and consumption in a Black-Scholes market with Levy-driven stochastic coefficients

• 成果类型: Article
• 署名作者: Delong, Lukasz; Klueppelberg, Claudia
• 署名单位: Warsaw School of Economics; Technical University of Munich
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/07-AAP475
• 发表日期: 2008
• 页码: 879-908
• 关键词: optimal portfolios; volatility; models; time

摘要

In this paper, we investigate an optimal investment and consumption problem for an investor who trades in a Black-Scholes financial market with stochastic coefficients driven by a non-Gaussian Ornstein-Uhlenbeck process. We assume that an agent makes investment and consumption decisions based on a power utility function. By applying the usual separation method in the variables, we are faced with the problem of solving a nonlinear (semilinear) first-order partial integro-differential equation. A candidate solution is derived via the Feynman-Kac representation. By using the properties of an operator defined in a suitable function space, we prove uniqueness and smoothness of the solution. Optimality is verified by applying a classical verification theorem.