Optimal portfolio, consumption and retirement decision under a preference change

Kwak, Minsuk; Shin, Yong Hyun; Choi, U Jin

doi:10.1016/j.jmaa.2009.02.004

Cited by 12 publications

(4 citation statements)

References 16 publications

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“…When the parents are alive, we can solve V using a method similar to the post-death period. As demonstrated by Equations ( 9) and (10), the optimal strategies are…”

Section: The Pre-death Periodmentioning

confidence: 99%

“…Duarte et al (2011) [9] continued this idea and extended the model to a multi-dimensional case with more economic interpretations. Kwak et al (2009) [10] explored the problem of evaluating OIC and OPT-LI for a family whose parents will receive deterministic work income until some deterministic time horizon. Considering the legacy between generations, Kwak et al (2011) [11] explored a business planning problem for a family consisting of parents and children.…”

Section: Introductionmentioning

confidence: 99%

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Optimal Investment–Consumption–Insurance Problem of a Family with Stochastic Income under the Exponential O-U Model

Wang,

Lin,

Chen

et al. 2023

Mathematics

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A household consumption and optimal portfolio problem pertinent to life insurance (LI) in a continuous time setting is examined. The family receives a random income before the parents’ retirement date. The price of the risky asset is driven by the exponential Ornstein–Uhlenbeck (O-U) process, which can better reflect the state of the financial market. If the parents pass away prior to their retirement time, the children do not have any work income and LI can be purchased to hedge the loss of wealth due to the parents’ accidental death. Meanwhile, utility functions (UFs) of the parents and children are individually taken into account in relation to the uncertain lifetime. The purpose of the family is to appropriately maximize the weighted average of the corresponding utilities of the parents and children. The optimal strategies of the problem are achieved using a dynamic programming approach to solve the associated Hamilton–Jacobi–Bellman (HJB) equation by employing the convex dual theory and Legendre transform (LT). Finally, we aim to examine how variations in the weight of the parents’ UF and the coefficient of risk aversion affect the optimal policies.

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“…When the parents are alive, we can solve V using a method similar to the post-death period. As demonstrated by Equations ( 9) and (10), the optimal strategies are…”

Section: The Pre-death Periodmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Optimal Investment–Consumption–Insurance Problem of a Family with Stochastic Income under the Exponential O-U Model

Wang,

Lin,

Chen

et al. 2023

Mathematics

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“…According to the results of the above studies, risk aversion tends to increase substantially at retirement. Kwak et al [ 13 ] considered risk aversion change at retirement, but did not impose any constraints (e.g., subsistence consumption constraint or borrowing constraint). Jang and Lee [ 10 ] investigated the combined effects of risk aversion change at retirement and borrowing constraints on the optimal consumption, portfolio, and retirement strategies.…”

Section: Introductionmentioning

confidence: 99%

Consumption-portfolio choice with subsistence consumption and risk aversion change at retirement

Lee

2018

J Inequal Appl

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This paper considers subsistence consumption of an economic agent both before and after retirement in analyzing the optimal consumption, portfolio, and retirement problem. We allow the relative risk aversion of the economic agent to make a one-off jump at retirement. With a Cobb–Douglas utility function, we obtain explicit expressions for the optimal policies. Numerical results show that, whereas post-retirement subsistence consumption tends to delay retirement, pre-retirement subsistence consumption and the magnitude of jump in relative risk aversion may stimulate early retirement. Also, the consumption drop at retirement deepens as post-retirement subsistence consumption increases, but it weakens as pre-retirement subsistence consumption increases.

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“…Since then, default-free portfolio optimization models have been extensively investigated in the literature (see, e.g., [4][5][6][7][8][9][10][11] and references therein). In [4], Fleming and Pang discussed a classical Merton portfolio optimization problem, where the interest rate r was assumed to be an ergodic Markov diffusion process.…”

Section: Introductionmentioning

confidence: 99%

Stochastic portfolio optimization with default risk

Bo¹,

Wang²,

Yang³

2013

Journal of Mathematical Analysis and Applications

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a b s t r a c tA stochastic portfolio optimization problem with default risk on an infinite time horizon is investigated. The default risk premium and the default intensity corresponding to the defaultable bond are assumed to rely on a stochastic factor formulated by a diffusion process. We study the optimal allocation and consumption policies to maximize the infinite horizon expected discounted non-log HARA utility of the consumption, and we use the dynamic programming principle to derive the Hamilton-Jacobi-Bellman (HJB) equation. Then we explore the HJB equation by employing a so-called sub-super solution approach. The optimal allocation and consumption policies are finally presented in a verification theorem, and also a numerical simulation is given at the end of the paper.

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Optimal portfolio, consumption and retirement decision under a preference change

Cited by 12 publications

References 16 publications

Optimal Investment–Consumption–Insurance Problem of a Family with Stochastic Income under the Exponential O-U Model

Optimal Investment–Consumption–Insurance Problem of a Family with Stochastic Income under the Exponential O-U Model

Consumption-portfolio choice with subsistence consumption and risk aversion change at retirement

Stochastic portfolio optimization with default risk

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