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This paper studies the retirement decision, optimal investment and consumption strategies under habit persistence for an agent with the opportunity to design the retirement time. The optimization problem is formulated as an interconnected optimal stopping and stochastic control problem (Stopping-Control Problem) in a finite time horizon. The problem contains three state variables: wealth $x$, habit level $h$ and wage rate $w$. We aim to derive the retirement boundary of this wealth-habit-wage triplet $(x,h,w)$. The complicated dual relation is proposed and proved to convert the original problem to the dual one. We obtain the retirement boundary of the dual variables based on an obstacle-type free boundary problem. Using dual relation we find the retirement boundary of primal variables and feed-back forms of optimal strategies. We show that if the so-called de facto wealth exceeds a critical proportion of wage, it will be optimal for the agent to choose to retire immediately. In numerical applications, we show how de facto wealth determines the retirement decisions and optimal strategies. Moreover, we observe discontinuity at retirement boundary: investment proportion always jumps down upon retirement, while consumption may jump up or jump down, depending on the change of marginal utility. We also find that the agent with higher standard of life tends to work longer.
In this paper,we study the individuals optimal retirement time and optimal consumption under habitual persistence. Because the individual feels equally satisfied with a lower habitual level and is more reluctant to change the habitual level after ret
We extend the result of our earlier study [Angoshtari, Bayraktar, and Young; Optimal consumption under a habit-formation constraint, available at: arXiv:2012.02277, (2020)] to a market setup that includes a risky asset whose price process is a geomet
This paper studies an optimal investment and consumption problem with heterogeneous consumption of basic and luxury goods, together with the choice of time for retirement. The utility for luxury goods is not necessarily a concave function. The optima
In this article we solve the problem of maximizing the expected utility of future consumption and terminal wealth to determine the optimal pension or life-cycle fund strategy for a cohort of pension fund investors. The setup is strongly related to a
We propose a new optimal consumption model in which the degree of addictiveness of habit formation is directly controlled through a consumption constraint. In particular, we assume that the individual is unwilling to consume at a rate below a certain