Life Insurance Demand under Health Shock Risk

Hambel, Christoph; Kraft, Holger; Schendel, Lorenz S.; Steffensen, Mogens

doi:10.2139/ssrn.2392384

Cited by 2 publications

(6 citation statements)

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“…In Kraft, Schendel, and Steffensen (2014), we consider a suchlike model where a family faces the risk of a health shock or an early death and has the possibility to contract a term life insurance to partially mitigate the risk of losing the wage earner's income. Similar analyses can be done by considering critical illness insurance or disability insurance.…”

Section: Resultsmentioning

confidence: 99%

“…They include a life insurance and focus especially on a correlation between labor income and the stock market. To the best of my knowledge, Kraft, Schendel, and Steffensen (2014) is the only continuous-time paper with a realistically calibrated life cycle and stochastic mortality risk. They include health jumps which increase the mortality risk significantly.…”

Section: Literaturementioning

confidence: 99%

“…6 The health jump calibration is taken from Kraft, Schendel, and Steffensen (2014) where it is described in detail. Thus, I set the health jump intensity to Figure 2 depicts the empirical mortality pattern, compared to the resulting mortality patterns of the S, SD and SDJ calibration.…”

Section: Mortality Riskmentioning

confidence: 99%

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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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Section: Resultsmentioning

confidence: 99%

Section: Literaturementioning

confidence: 99%

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Consumption-Investment Problems with Stochastic Mortality Risk

Schendel

2014

SSRN Journal

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“…Mortality Risk I use the mortality process and mortality shock calibration of Kraft, Schendel, and Steffensen (2014 The figure compares the average health expenses after 1 000 000 simulations (line) with the data for Germany (points). The calibration for the simulated results is stated in Section 3.…”

Section: Calibrationmentioning

confidence: 99%

“…I use the average administrative fee (2.99%) and transaction fee (5.05%) given in Kraft, Schendel, and Steffensen (2014). These are the average values for German life insurance companies in 2011.…”

Section: Insurance Demandmentioning

confidence: 99%

Critical Illness Insurance in Life Cycle Portfolio Problems

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. Terms of use: Documents in Non-Technical SummaryThe first critical illness (CI) insurance (also known as dread disease insurance) was developed in South Africa in 1983. The insurance pays a previously fixed lump sum if the insured person is diagnosed with a critical illness from a list of insured illnesses. Although the CI insurance is becoming more popular, it is still rarely used in Germany compared with disability insurance or other health-related insurance products. The relatively low demand for CI insurance is surprising due to the possible benefits. To give an example, blindness or deafness are critical illnesses that are often covered by a CI insurance. These illnesses might or might not trigger a disability insurance and lead to large costs that are not fully covered by a health insurance. A handicapped-accessible house, books for blind persons, or a special computer produce large costs. Since the expected lifetime is usually not reduced, this messes up the financial planning. I model such illnesses with health shocks in the model. Cancer or a heart attack are examples for insurable critical illnesses that reduce the expected remaining lifetime and might or might not trigger a disability insurance as well. These illnesses also produce large costs, e.g. for medicine and health care. Mortality shocks in my model capture such illnesses. The seemingly huge benefits of the CI insurance raise the question why there is little demand for this type of insurance. To the best of my knowledge, there is no life cycle model explicitly considering such an insurance.I consider a life cycle consumption-investment-insurance problem in continuous time. The agent has to pay exogenously determined health expenses that can jump due to a critical illness of the agent. In order to avoid the excess health expenses, the agent can contract a CI insurance. The agent receives unspanned labor income and decides about the optimal consumption, investment, and insurance strategy. The financial market consists of a riskless bond and a stock. The time of death is random. The hazard rate of death can jump due to a mortality shock. A critical illness may lead to an increased mortality risk but this is not necessarily the case. In this work, I analyze whether the agent wants to contract the CI insurance or not. Moreover, I investigate the driving factors of the resulting CI insurance demand.The increased health expenses due to a shock have a crucial impact both for the aggregate resu...

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Life Insurance Demand under Health Shock Risk

Cited by 2 publications

References 25 publications

Consumption-Investment Problems with Stochastic Mortality Risk

Consumption-Investment Problems with Stochastic Mortality Risk

Critical Illness Insurance in Life Cycle Portfolio Problems

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