Optimal investment and consumption decision of a family with life insurance

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

doi:10.1016/j.insmatheco.2010.10.012

Cited by 49 publications

(28 citation statements)

References 26 publications

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“…In the same vein Pliska [28] studied optimal life insurance and consumption for an income earner whose lifetime is random and unbounded. More recently Kwak et al [18] looked at the problem of finding optimal investment and consumption for a family whose parents receive deterministic labor income until some deterministic time horizon.…”

Section: Introductionmentioning

confidence: 99%

Time-Consistent Portfolio Management

Ekeland¹,

Mbodji²,

Pirvu³

2012

SIAM J. Finan. Math.

137

100

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Abstract. This paper considers the portfolio management problem for an investor with finite time horizon who is allowed to consume and take out life insurance. Natural assumptions, such as different discount rates for consumption and life insurance lead to time inconsistency. This situation can also arise when the investor is in fact a group, the members of which have different utilities and/or different discount rates. As a consequence, the optimal strategies are not implementable. We focus on hyperbolic discounting, which has received much attention lately, especially in the area of behavioural finance. Following [10], we consider the resulting problem as a leader-follower game between successive selves, each of whom can commit for an infinitesimally small amount of time. We then define policies as subgame perfect equilibrium strategies. Policies are characterized by an integral equation which is shown to have a solution in the case of CRRA utilities. Our results can be extended for more general preferences as long as the equations admit solutions. Numerical simulations reveal that for the Merton problem with hyperbolic discounting, the consumption increases up to a certain time, after which it decreases; this pattern does not occur in the case of exponential discounting, and is therefore known in the litterature as the "consumption puzzle". Other numerical experiments explore the effect of time varying aggregation rate on the insurance premium.

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Section: Introductionmentioning

confidence: 99%

Time-Consistent Portfolio Management

Ekeland¹,

Mbodji²,

Pirvu³

2012

SIAM J. Finan. Math.

137

100

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“…They calculate the corresponding optimal consumption, investment and insurance decision. Kwak, Shin, and Choi (2011) consider the life insurance purchase of a family as well. They use a HARA utility as a weighted average from parents' and children's utility.…”

Section: Literaturementioning

confidence: 99%

Consumption-Investment Problems with Stochastic Mortality Risk

Schendel

2014

SSRN Journal

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Standard-Nutzungsbedingungen:Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden.Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich machen, vertreiben oder anderweitig nutzen.Sofern die Verfasser die Dokumente unter Open-Content-Lizenzen (insbesondere CC-Lizenzen) zur Verfügung gestellt haben sollten, gelten abweichend von diesen Nutzungsbedingungen die in der dort genannten Lizenz gewährten Nutzungsrechte. www.econstor.eu Terms of use: Documents in Non-Technical SummaryLife cycle consumption-investment models often assume a deterministic time of death or, if at all, include deterministic mortality risk given by mortality tables. Only a few recent papers allow for stochastic mortality risk driven by a diffusive component. In reality, cancer and other critical illnesses suggest that there is a significant jump component in the individual hazard rate of death that is not captured by the life cycle consumption-investment models. This raises the question of the importance of mortality risk in life cycle consumption-investment models, and what impact a jump component in the hazard rate of death has. My paper aims to close this gap in the literature.The main feature of my model is the uncertain time of death due to mortality risk. Mortality risk is rarely considered in continuous-time life cycle models, whereas it is often analyzed in the insurance literature. The main difference between the life cycle and the insurance perception of mortality risk is that the insurance literature considers aggregate mortality rates. In contrast, in the individual consumption-investment decision, I focus on an agent's perspective and consider the individual mortality risk of an agent. This difference affects both interpretation and modeling. If the actuarial literature considers jumps, it focuses mostly on negative jumps since these yield decreased profits of annuities. Furthermore, it considers jumps in aggregate mortality rates. In my model, individual positive shocks that occur with higher intensity are more important. These can be interpreted as health problems with a permanent impact, e.g. medical disasters like a cancer detection or an accident.I analyze the impact of mortality risk in a life cycle consumption-investment model. Further model features are unspanned labor income risk, short-sale and liquidity constraints and a simple insurance. The mortality process is calibrated to mortality data for Germany and allows uncertainty driven by a diffusive and jump component. I compare results with deterministic time of death and stochastic time of death. Furthermore, I provide sensitivity analyses with respect to the agent's characteristics and the financial market. I also analyze the impact of the insurance and of a bequest motive.The mortality calibration shows that allowing for jumps in the hazard rate of death significantly increases the fit to the data. Considering the resu...

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“…The problem of finding the optimal strategy for purchasing life insurance has not been studied nearly as much as the corresponding problem for life annuities; see Milevsky and Young (2007) and the many references therein for research dealing with life annuities. Notable exceptions are the seminal papers of Richard (1975) and Campbell (1980) and the more recent papers of Pliska and Ye (2007), Huang and Milevsky (2008), Kraft and Steffensen (2008), Nielsen and Steffensen (2008), Wang et al (2010), Kwak, Shin, and Choi (2011), Bruhn and Steffensen (2011), and Egami and Iwaki (2011). We highlight the last two articles because that work is closely related to the work in this paper.…”

Section: Introductionmentioning

confidence: 95%

Life Insurance Purchasing to Maximize Utility of Household Consumption

Bayraktar

Young

2013

North American Actuarial Journal

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We determine the optimal amount of life insurance for a household of two wage earners. We consider the simple case of exponential utility, thereby removing wealth as a factor in buying life insurance, while retaining the relationship among life insurance, income, and the probability of dying and thus losing that income. For insurance purchased via a single premium or premium payable continuously, we explicitly determine the optimal death benefit. We show that if the premium is determined to target a specific probability of loss per policy, then the rates of consumption are identical under single premium or continuously payable premium. Thus, not only is equivalence of consumption achieved for the households under the two premium schemes, it is also obtained for the insurance company in the sense of equivalence of loss probabilities.

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Optimal investment and consumption decision of a family with life insurance

Cited by 49 publications

References 26 publications

Time-Consistent Portfolio Management

Time-Consistent Portfolio Management

Consumption-Investment Problems with Stochastic Mortality Risk

Life Insurance Purchasing to Maximize Utility of Household Consumption

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