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This paper studies the life cycle consumption-investment-insurance problem of a family. The wage earner faces the risk of a health shock that significantly increases his probability of dying. The family can buy long-term life insurance that can only be revised at significant costs, which makes insurance decisions sticky. Furthermore, a revision is only possible as long as the insured person is healthy. A second important feature of our model is that the labor income of the wage earner is unspanned. We document that the combination of unspanned labor income and the stickiness of insurance decisions reduces the long-term insurance demand significantly. This is because an income shock induces the need to reduce the insurance coverage, since premia become less affordable. Since such a reduction is costly and families anticipate these potential costs, they buy less protection at all ages. In particular, young families stay away from long-term life insurance markets altogether. Our results are robust to adding short-term life insurance, annuities and health insurance.
This paper studies the life cycle consumption-investment-insurance problem of a family. The wage earner faces the risk of a health shock that significantly increases his probability of dying. The family can buy term life insurance with realistic features. In particular, the available contracts are long term so that decisions are sticky and can only be revised at significant costs. Furthermore, a revision is only possible as long as the insured person is healthy. A second important and realistic feature of our model is that the labor income of
the wage earner is unspanned. We document that the combination of unspanned labor income and the stickiness of insurance decisions reduces the insurance demand significantly. This is because an income shock induces the need to reduce the insurance coverage, since premia become less affordable. Since such a reduction is costly and families anticipate these potential costs, they buy less protection at all ages. In particular, young families stay away from life insurance markets altogether.
I analyze a critical illness insurance in a consumption-investment model over the life cycle. I solve a model with stochastic mortality risk and health shock risk numerically. These shocks are interpreted as critical illness and can negatively affect the expected remaining lifetime, the health expenses, and the income. In order to hedge the health expense effect of a shock, the agent has the possibility to contract a critical illness insurance. My results highlight that the critical illness insurance is strongly desired by the agents. With an insurance profit of 20%, nearly all agents contract the insurance in the working stage of the life cycle and more than 50% of the agents contract the insurance during retirement. With an insurance profit of 200%, still nearly all working agents contract the insurance, whereas there is little demand in the retirement stage.
I numerically solve realistically calibrated life cycle consumption-investment problems in continuous time featuring stochastic mortality risk driven by jumps, unspanned labor income as well as short-sale and liquidity constraints and a simple insurance. I compare models with deterministic and stochastic hazard rate of death to a model without mortality risk. Mortality risk has only minor effects on the optimal controls early in the life cycle but it becomes crucial in later years. A diffusive component in the hazard rate of death has no significant impact, whereas a jump component is desired by the agent and influences optimal controls and wealth evolution. The insurance is used to ensure optimal bequest such that there is no accidental bequest. In the absence of the insurance, the biggest part of bequest is accidental.
Die Dissertation besteht aus drei thematisch zusammenhängenden Forschungspapieren, in denen zeitstetige Konsum-, Investment- und Versicherungsprobleme über den Lebenszyklus betrachtet werden. Ein besonderer Fokus liegt auf realistischen Features wie stochastischem Sterberisiko und nicht-replizierbarem Einkommen. In der ersten Forschungsarbeit untersuche ich die Relevanz von stochastischem Sterberisiko. Dabei zeige ich, dass eine Sprungkomponente in der Sterberate die optimalen Entscheidungen der Agenten und das Wohlfahrtslevel signifikant beeinflusst. Eine Diffusionskomponente ist hingegen vernachlässigbar. In dem zweiten Forschungspapier untersuchen wir die Risikolebensversicherungsnachfrage einer Familie, dessen Alleinverdiener stochastischem Sterberisiko ausgesetzt ist. Wir achten insbesondere auf eine realistische Modellierung der Versicherung. Wir zeigen, dass dadurch junge Agenten dem Versicherungsmarkt fern bleiben und die Versicherungsnachfrage mit dem Alter steigt, im Gegensatz zu Modellen mit einfachen stetig-veränderbaren Versicherungen. Weiterhin verstärken langlaufende Versicherungsverträge die negativen Effekte von Einkommensschocks und werden daher von risikoaversen Agenten weniger abgeschlossen. In der dritten Forschungsarbeit untersuche ich die Critical Illness Versicherungsnachfrage eines Agenten in einem Modell mit stochastischem Sterberisiko und Gesundheitsausgaben. Die Versicherung übernimmt dabei die zusätzlichen Gesundheitskosten, die bei einem Sprung entstehen. Fast alle Agenten schließen solch eine Versicherung vor dem Rentenalter ab, selbst wenn diese sehr kostspielig ist. Insbesondere Agenten mit geringen Gesundheitsausgaben und hohem Einkommen haben eine hohe Versicherungsnachfrage.
