We study an optimal retirement, consumption/portfolio selection problem of an economic agent in a non-Markovian environment. We show that under a suitable condition the optimal retirement decision is to retire when the individual’s wealth reaches a threshold level. We express the value and the optimal strategy by using the strong solution of the backward stochastic partial differential variational inequality (BSPDVI) associated with the dual problem. We derive properties of the value function and the optimal strategy by analyzing the strong solution and the free boundary of the BSPDVI. We also make a methodological contribution by proposing an approach to investigate properties of the strong solution and the stochastic free boundary of BSPDVI by combining a probabilistic method and the theory of backward stochastic partial differential equations (BSPDEs).

我们研究了非马尔可夫环境中经济主体的最优退休，消费/投资组合选择问题。我们表明，在合适的条件下，最佳退休决策是在个人财富达到阈值水平时退休。我们通过使用与对偶问题相关的反向随机偏微分变异性不等式（BSPDVI）的强解来表达价值和最优策略。通过分析BSPDVI的强解和自由边界，我们得出了价值函数和最优策略的属性。