通胀与生存约束下最优投资和自愿退休选择

An optimal investment and voluntary retirement choice problem with subsistence consumption constraints under inflation

研究在通胀下,代理人退休选择、最优消费和投资组合决策问题.运用伊藤公式(It■公式)推导了通胀折现的财富动力学方程,基于考虑退休前后的预期消费折现效用最大化标准,利用动态规划方法建立了相应的HJB方程,并求解出最优消费、投资组合与自愿退休选择策略.最后对理论结果给出数值模拟.结果表明,退休前,适当的通胀波动率会带动代理人积极投资,消费反而减少,若通胀波动率过大,代理人会减少投资增加消费来预防通胀风险带来的损失;退休后,代理人的投资和消费均会增加.研究结果对投资者具有参考价值.

This paper investigates the optimal consumption/portfolio and retirement problem of an agent under inflation.By using It■ formula,the real wealth process discounted by inflation is derived.Based on maximizing the expected discounted utility of consumption both before and after retirement,the corresponding HJB equations are established by applying the dynamic programming method.Furthermore,the strategies for the optimal consumption,portfolio investment and retirement are derived.Finally,a numerical analysis is provided.The result shows that before retirement,the investment of the agent may increase and the consumption may decrease when inflation volatility is appropriate.If the inflation volatility is high,the investment of the agent may decrease and the consumption may increase to provide for the inflation losses.After retirement,both the consumption and investment of the agent may increase.The result of the paper has important reference values for investors.