Finite-horizon optimal consumption and investment problem with a preference change

Park, Kyunghyun; Jeon, Junkee

doi:10.1016/j.jmaa.2018.12.023

Cited by 4 publications

(4 citation statements)

References 9 publications

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“…In order to separate the stopping time and stochastic controls, we first define the dual functions of "running utility" U 1 and "terminal utility" Ū , respectively. By the dual approach, Problem (3.3) can be transformed to a pure optimal stopping problem (see Park and Jeon (2019), Yang and Koo (2018), Liang, Peng, andGuo (2014), Choi, Shim, andShin (2008) or Karatzas and Wang (2000) for such a transformation). After obtaining the optimal stopping problem, we construct the corresponding variational inequality.…”

Section: Habit Reduction Methodmentioning

confidence: 99%

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Retirement decision and optimal consumption-investment under addictive habit persistence

Guan¹,

Liang²,

Yuan³

2020

Preprint

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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.

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Section: Habit Reduction Methodmentioning

confidence: 99%

“…In either case, researchers aim at finding thresholds for wealth (or factors) that push the agent to retire. This topic remains very active recently, see Yang and Koo (2018), Park and Jeon (2019), Yang, Koo, and Shin (2020), Jang, Park, and Zhao (2020), Xu and Zheng (2020), etc.…”

Section: Introductionmentioning

confidence: 99%

Retirement decision and optimal consumption-investment under addictive habit persistence

Guan¹,

Liang²,

Yuan³

2020

Preprint

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“…Note that our model's two features-government subsidy and labor flexibility-obscure the duality relationship of the primal and the dual value and make it difficult to characterize the free boundaries corresponding to the stopping time. Borrowing arguments from Knudsen et al (1998) and the standard methods of optimal stopping problems from Yang and Koo (2018) and Park and Jeon (2019), in Appendix 2, we fully characterize the free boundary problem and show that the optimal dual boundary for retirement is given bȳ…”

Section: J(y)mentioning

confidence: 99%

“…Since the study by Karatzas and Wang (2000), the bulk of the literature (e.g. Peskir and Shiryaev 2006, Yang and Koo 2018, Park and Jeon 2019 considered both stochastic control and optimal stopping time. We adopt a duality/martingale method to derive the optimal policies and threshold wealth level for retirement (see e.g.…”

Section: Introductionmentioning

confidence: 99%

Effects of a government subsidy and labor flexibility on portfolio selection and retirement

Park

Lee²,

Shin

2021

Quantitative Finance

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We address the ways in which a government subsidy and labor flexibility affect optimal policies and retirement decisions using a continuous-time theoretical model with endogenous labor/leisure choice. In response to a government subsidy, working agents increase their overall consumption, leisure spending, and investment in risky assets, which is an intuitive finding. Labor flexibility has marginal effects on consumption and leisure when an agent's wealth is insufficient. However, when a working agent has enough wealth to enjoy maximum leisure, labor flexibility increases leisure spending and reduces risky investments. The impacts of the two features conflict in terms of retirement decisions (i.e. the optimal threshold wealth level is decreased by the subsidy and increased by labor welfare), while labor flexibility takes precedence. Furthermore, the government subsidy is more impactful in a bad economy than in a good economy.

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Optimal retirement and portfolio selection with consumption ratcheting

Jeon

Park

2020

Math Finan Econ

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Finite-horizon optimal consumption and investment problem with a preference change

Cited by 4 publications

References 9 publications

Retirement decision and optimal consumption-investment under addictive habit persistence

Retirement decision and optimal consumption-investment under addictive habit persistence

Effects of a government subsidy and labor flexibility on portfolio selection and retirement

Optimal retirement and portfolio selection with consumption ratcheting

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