带有随机收入与时变风险厌恶系数的最优投资-消费问题

本文考虑具有随机收入与时变相对风险厌恶系数的消费者的最优投资-消费问题.假定消费者参与工作获得工资,进行消费并将财富投资到一个风险资产和一个无风险资产,目标是最大化工作期消费和退休时刻财富的期望效用.其中,工资过程是随机的并服从一个几何布朗运动,在不同时刻,消费者对消费的偏好由一个时变的风险厌恶系数刻画.本文假定金融市场是完备的,采用鞅方法求解,得到最优消费与投资的解析表达式,并对最优消费和投资策略进行敏感性分析.结果表明,当消费者拥有时变风险厌恶系数时,初始财富的大小对其最优期望消费路径影响很大.当消费者面临工资风险时,投资策略中出现了新的对冲项.当消费者流动性财富增大时,消费者消费-收入比增大,但绝对消费水平的变化不确定.

Optimal investment and consumption choice with stochastic income and time-varying risk aversion

This paper considers the optimal consumption-investment strategy for a consumer receiving stochastic salary and having time-varying relative risk aversion. We assume that the consumer participates in the labor market, receives salary, consumes and invests her wealth in a risky stock and a risk-free bond, with the goal of maximizing the expected utility from both the future consumption and the terminal wealth at retirement. We define the stochastic salary process as a geometric Brownian motion, and assume her relative risk aversion to be time-varying. In our model, the financial market is complete and we provide an analytical characterization of the optimal consumption-investment strategy using the martingale approach. Furthermore, we present some sensitivity analysis of the optimal strategy. Our results show that when facing a time-varying relative risk aversion, the initial wealth plays a significant role in the consumer's optimal consumption. What is more, a new composition to hedge the salary risk exits in her optimal investment strategy, and when her liquid wealth level grows, the consumption-income ratio increases, but the change of her consumption is uncertain.