Consumption-Investment Problems with Stochastic Mortality Risk

Abstract

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...

Critical Illness Insurance in Life Cycle Portfolio Problems

“…The numerical approach is similar to the one used in Schendel (2014) which is based on the procedure in Munk and Sørensen (2010). Details considering the numerical method are given in the papers mentioned above.…”