Optimal Consumption and Investment in an Incomplete Market with Hedgeable Stochastic Income

This paper studies the optimal investment and consumption problem with stochastic income in an incomplete market. We formulate a general model in which the financial market is itself incomplete and the income risk is correlated with the market risk. The economic agent exhibits a general class of utility functions with respect to consumption and terminal wealth. Applying the duality techniques, the optimal consumption and investment strategies and optimal Equivalent Martingale Measure (EMM) for such incomplete market setting are investigated. In addition, we define a class of hedgeable stochastic income whose volatility can be represented in terms of volatility coefficients matrix of risk assets. An important example is that the log return of stochastic income can be linearly expressed by the log return of risk assets in the financial market. We show that hedgeable stochastic income is the sufficient and necessary condition of deterministic optimal EMM, and then the optimal consumption and investment policies can be explicitly obtained under hedgeable stochastic income. As an application, we present the optimal heterogeneous consumption and investment for an agent with CARA Utility. At last, numerical studies are given to illustrate some economic implications of the results.

报告人简介:周明，中国人民大学统计学院风险管理与精算系教授、博士研究生导师，中国人民大学应用统计科学研究中心研究员，风险管理与精算研究中心主任。感兴趣的研究领域包括风险管理与精算、风险分析与决策、投资消费与保险需求，最优保险与再保险等。在国内外学术期刊发表论文50余篇，主持国家、省部级课题和企业委托课题共计10余项。现为北美准精算师（ASA），中国精算师协会理事、正会员、教育考试委员会委员，中国现场统计研究会教育统计与管理分会常务理事，中国工业与应用数学学会金融数学与金融工程和精算保险专业委员会委员。