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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.
In this paper, we consider the optimal investment-consumption problem for consumers with stochastic income and time-varying relative risk aversion. Assuming that consumers are involved in work to obtain wages, consume and invest wealth to a risk-free asset and a risk-free asset, the objective is to maximize The consumption of retirement work and the expected utility of the moment of retirement.While the wage process is random and subject to a geometric Brownian motion, at different times, consumer preferences are characterized by a time-varying risk aversion.This paper assumes that the financial markets Is complete, and is solved by martingale method to get the analytical expression of the optimal consumption and investment, and the sensitivity analysis of the optimal consumption and investment strategy.The results show that when consumers have time-varying risk aversion coefficient, the initial wealth Size has a great influence on the optimal expected consumption path.When consumers face salary risk, new hedging items appear in the investment strategy.When consumers’ liquidity wealth increases, the consumer’s consumption-income ratio increases, but The level of absolute consumption is not certain.