考虑红利和退休的最优消费-投资和遗产问题

摘要

The problem of the optimal consumption and portfolio with the investor's heritage and insurance, in which the stocks have dicidend-paying under three different borrowing constraints, is studied. Firstly, the policies of the optimal consumption-portfolio and bequest of investors are explicitly provided by using of the stochastic differential equations and the martingale method. Secondly, through the numerical simulation, both the changes of the investment and consumption ratios are analyzed under the three different borrowing constraints. Finally, the effect of the dividends on investment and consumption is discussed.%在股票支付红利的情况下,考虑投资者遗产并结合保险,研究3种不同的借贷约束下的消费与投资问题.首先,借助随机微分方程求解投资者最优消费和投资策略的显式表达式,其次,结合数值分析,说明3种约束情形下投资占总财富比率以及消费占总财富比率对于财富的变化趋势,最后,研究了股票是否支付红利对投资比率以及消费比率的影响.