Optimal life insurance purchase and consumption/investment under uncertain lifetime

Pliska, Stanley R.; Ye, Jinchun

doi:10.1016/j.jbankfin.2006.10.015

Cited by 164 publications

(105 citation statements)

References 7 publications

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“…Second, as Leung (1994) pointed out, there is a problem with the existence of interior solutions. In order to overcome these difficulties, Pliska and Ye (2007) incorporated the randomness of the planning horizon by means of the uncertain life model found in reliability theory. In contrast to Richard (1975), in which the random lifetime took values on a bounded interval, in that paper the authors considered an intertemporal model and allowed the random lifetime to take values on [0, ∞).…”

Section: Introductionmentioning

confidence: 99%

“…Second, at T a utility was introduced accounting for the agent wealth at the final time. After setting up the HJB equation and deriving the optimal feedback control law, Pliska and Ye (2007) obtained explicit solutions for the family of discounted CRRA utilities. As it is customary in the analysis of intertemporal decision problems, the decision maker considered was characterized by a constant discount rate of time preference, i.e., she discounted the stream of utilities of any category using an exponential discount function with a constant discount rate of time preference according to the Discounted Utility (DU) model introduced in Samuelson (1937).…”

Section: Introductionmentioning

confidence: 99%

“…Along the same lines, Karp (2007) and Marín-Solano and Navas (2010) dealt with the problem with nonconstant discounting. Also, in a recent paper by Ekeland et al (2012), the model of Pliska and Ye (2007) was extended with the introduction of non-constant discount rates.…”

Section: Introductionmentioning

confidence: 99%

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Consumption, Investment and Life Insurance Strategies with Heterogeneous Discounting

et al. 2012

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In this paper we analyze how the optimal consumption, investment and life insurance rules are modified by the introduction of a class of time-inconsistent preferences. In particular, we account for the fact that an agent's preferences evolve along the planning horizon according to her increasing concern about the bequest left to her descendants and about her welfare at retirement. To this end, we consider a stochastic continuous time model with random terminal time for an agent with a known distribution of lifetime under heterogeneous discounting. In order to obtain the timeconsistent solution, we solve a non-standard dynamic programming equation. For the case of CRRA and CARA utility functions we compare the explicit solutions for the time-inconsistent and the time-consistent agent. The results are illustrated numerically. AbstractEn aquest treball s'analitza l'efecte que comporta l'introducció de preferències inconsistents temporalment sobre les decisionsòptimes de consum, inversió i compra d'assegurança de vida. En concret, es pretén recollir la creixent importància que un individu dóna a la herència que deixa i a la riquesa disponible per a la seva jubilació al llarg de la seva vida laboral. Amb aquesta finalitat, es parteix d'un model estocàstic en temps continu amb temps final aleatori, i s'introdueix el descompte heterogeni, considerant un agent amb una distribució de vida residual coneguda. Per tal d'obtenir solucions consistents temporalment es resol una equació de programació dinàmica no estàndard. Per al cas de funcions d'utilitat del tipus CRRA i CARA es troben solucions explícites. Finalment, els resultats obtinguts s'il·lustren numèricament.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Consumption, Investment and Life Insurance Strategies with Heterogeneous Discounting

et al. 2012

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“…(See Pliska and Ye [16].) Figure 1 illustrates the optimal policies : consumption of parents, consumption of children, portfolio(investment in risky asset), life insurance premium at time t = 0 with γ p = γ c = 2.…”

Section: Numerical Examplementioning

confidence: 99%

“…Recently, Pliska and Ye [16] studied an optimal life insurance and consumption for an individual whose lifetime is random and receives labor income, but did not consider investment in risky asset. Ye [20] considered an optimal life insurance, consumption and portfolio choice problem under uncertain lifetime and solved the problem using martingale method which we used to solve our problem.…”

Section: Introductionmentioning

confidence: 99%

Optimal investment and consumption decision of a family with life insurance

Kwak

Shin

Choi

2011

Insurance: Mathematics and Economics

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We study an optimal portfolio and consumption choice problem of family that combines life insurance of parents who receive deterministic labor income until fixed time horizon T . We consider utility functions of parents and children separately and assumed that parents have uncertain lifetime. If parents die before T , children have no income and they choose the optimal consumption and portfolio with remaining wealth combining the insurance benefit. Before the death time of parents, the object of family is to maximize weighted average of utility of parents and children. It is assumed that the utility function of both parents and children belong to HARA utility class. Using HARA utility we impose the condition that instantaneous consumption rate should be above a given lower bound.We analyze how the change of weight and other parameters such as lower bound of consumption, income process, hazard rate affect the optimal policies using various numerical examples. * We are grateful to Hyeng Keun Koo and Jaeyoung Sung for useful comments and advice.

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An equivalent approximation approach for the Hamilton‐Jacobi‐Bellman equations in intertemporal decision problems

Xiang

Chen

2018

Optim Control Appl Methods

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In this paper, we develop an equivalent approximation approach to obtain the Hamilton-Jacobi-Bellman (HJB) equations of intertemporal decision problems under uncertainty. An implicit discount function is adopted in the derivation of the rate of change of value function for the HJB equations to provide the broadest coverage of time preferences. Meanwhile, we provide an illustrative example for application by revisiting the intertemporal consumption and portfolio decisions problem. Furthermore, we verify the validity of our approach in robustness tests by incorporating exponential, nonconstant, and stochastic hyperbolic discounting functions, respectively. The HJB equations and their resulting decision rules in the finite and infinite planning horizons have confirmed that our approach provides an efficient and reliable alternative to acquire the HJB equations in the intertemporal economic issues under uncertainty. KEYWORDS equivalent approximation, HJB equation, intertemporal decision, time inconsistency 1976

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Optimal life insurance purchase and consumption/investment under uncertain lifetime

Cited by 164 publications

References 7 publications

Consumption, Investment and Life Insurance Strategies with Heterogeneous Discounting

Consumption, Investment and Life Insurance Strategies with Heterogeneous Discounting

Optimal investment and consumption decision of a family with life insurance

An equivalent approximation approach for the Hamilton‐Jacobi‐Bellman equations in intertemporal decision problems

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