We analyze a family's term life insurance demand in a life cycle portfolio choice model. A major source of risk for a family is the early death of the sole wage earner. To hedge this, the family in our model can contract a term life insurance. Most existing papers studying the life insurance demand consider short term contracts that can be bought or sold continuously which ensures an optimal insurance holding at each point in time. This simplification might crucially affect the results. Therefore, we focus on a model where the family can choose between different long-term contracts that differ with respect to their insurance sum. The annual insurance premium includes fees for administrative costs and transaction costs. A belated change of the insurance is costly for the family and only possible as long as the insured person is younger than a specific age and healthy. The wage earner faces stochastic mortality risk with a jump component that we interpret as critical illness. Once the agent suffers from a critical illness, the family cannot change the insurance contract any more, the income of the family reduces, and the mortality risk increases. If the wage earner dies before the maturity of the insurance contract, the remaining family members receive a single, fixed payment of the insurance company. We use a German life table to calibrate the mortality process, German cancer data to calibrate the critical illness shock and data of the German life insurance industry to calibrate the insurance fees. The insurance premiums are calculated such that the contracts are actuarially fair.The realistically modeled insurance induces new qualitative effects that are important for the optimal decisions over the life cycle. The long-term insurance contract amplifies the effect of negative labor income shocks, since in the undesired case of a negative labor income shock a premature termination of the contract or a reduction of the insurance sum leads to additional losses. In an already bad state, the family has problems to make the premium payments. Families with a lower income volatility have a significantly higher insurance demand. The amplifying effect also reduces the insurance demand of families that are more risk averse. In general, the families increase insurance protection over the life cycle. The long term contract design effect fades away as agents get older, since the contract duration and human wealth uncertainty reduce. Most importantly, young families do not buy any long-term term life insurance. If an older agent suddenly dies, the accumulated financial wealth and contracted insurance ensures that the surviving family member can maintain their consumption level, although consumption growth is reduced. By contrast, an unexpected death in younger years leads to severe problems for the family.Our results are robust to adding short-term insurance, annuities, or health insurance. For instance, if families have also access to short-term insurance, they buy these contracts at a young age without demanding long-term ins...

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 EconStor may www.econstor.euElectronic copy available at: http://ssrn.com/abstract=2392384Electronic copy available at: http://ssrn.com/abstract=2392384 Non-Technical SummaryWe analyze a family's term life insurance demand in a life cycle portfolio choice model. A major source of risk for a family is the early death of the sole wage earner. To hedge this, the family in our model can contract a term life insurance. Most existing papers studying the life insurance demand consider short term contracts that can be bought or sold continuously which ensures an optimal insurance holding at each point in time. This simplification might crucially affect the results. Therefore, we focus on a more realistic model for the insurance contract. The family can choose between different long-term contracts that differ with respect to their insurance sum. The annual insurance premium includes fees for administrative costs and transaction costs. A belated change of the insurance is costly for the family and only possible as long as the insured person is younger than a specific age and healthy. The wage earner faces stochastic mortality risk with a jump component that we interpret as critical illness. Once the agent suffers from a critical illness, the family cannot change the insurance contract any more, the income of the family reduces, and the mortality risk increases. If the wage earner dies before the maturity of the insurance contract, the remaining family members receive a single, fixed payment of the insurance company. We use a German life table to calibrate the mortality process, German cancer data to calibrate the critical illness shock and data of the German life insurance industry to calibrate the insurance fees. The insurance premiums are calculated such that the contracts are actuarially fair.The realistically modeled insurance induces new qualitative effects that are important for the optimal decisions over the life cycle. The long-term insurance contract amplifies the effect of negative labor income shocks, since in the undesired case of a negative labor income shock a premature termination of the contract or a reduction of the insurance sum leads to additional losses. In an already bad state, the family has problems to make the premium payments. Families with a lower income volatility have a significantly higher insurance demand. The amplifying effect also reduces the insurance demand of families that are more risk averse. In gener...

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...

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...