报告人：周明 教授（中国人民大学）

时间：2025年03月28日 10:00-

地点：数统学院LD718

摘要：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.

邀请人: 张志民

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