Consumption-portfolio Choice with Critical Illness

Project Start: 01/2014
Status: Completed
Researchers: Christoph Hambel, Holger Kraft, Mogens Steffensen, Sebastian Wagner, Farina Weiss
Category: Household Finance

Topic and Objectives

A major source of risk for a family is the early death of the sole wage earner. Families can hedge this risk by taking out a life insurance policy. Most existing research studying 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 life cycle portfolio choice model for the insurance contract (SAFE Working Paper No. 40).

In our model, 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 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 decreases, 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.

Key Findings

  • A more realistically modeled insurance contract crucially affects the results since new qualitative effects appear. Especially, the long-term nature of the contract amplifies the effects of negative 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 lead to additional losses.
  • In general, 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 decreases. Young families, however, do not buy any term life insurance. If an older agent suddenly dies, the accumulated financial wealth and contracted insurance ensures that the surviving family members 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.
  • A high level of income, a high labor income volatility, large fees imposed by insurance companies and the presence of health shocks reduce the insurance demand of a family. Also, the insurance demand of families that are more risk averse is reduced by the amplifying effect.
  • To avoid lifetime poverty of the remaining family members, a social security could mitigate those problems by making transfer payments. Of course, a more welfare optimal solution should provide an incentive for families to insure themselves, especially early in life where the potential gap is the biggest.
  • A contract with a variable insurance sum which is linked to the actual labor income evolution (like in practice often done in occupational pensions) could avoid the negative amplifying effects of labor income shocks.
  • SAFE Working Paper No. 44 shows that agents would strongly benefit from taking out a critical illness insurance policy to hedge jumps in health expenses, even if the insurance is very costly.

Related Published Papers

Author/s Title Year Research Area Keywords
Christoph Hambel, Holger Kraft, Lorenz Schendel, Mogens Steffensen Life Insurance Demand under Health Shock Risk
Journal of Risk and Insurance
2017 Household Finance Health shocks, Portfolio choice, Term life insurance, Mortality risk, Labor income risk

Related Working Papers

No. Author/s Title Year Research Area Keywords
40 Christoph Hambel, Holger Kraft, Lorenz Schendel, Mogens Steffensen Life Insurance Demand under Health Shock Risk 2014 Household Finance Health shocks, Portfolio choice, Term life insurance, Mortality risk, Labor income risk
44 Lorenz Schendel Critical Illness Insurance in Life Cycle Portfolio Problems 2014 Household Finance Health shocks, Health expenses, Labor income risk, Stochastic mortality risk, Portfolio choice

 

Back