Asset Demands and Consumption with Longevity Risk
Posted: 11 Nov 2010 Last revised: 24 Aug 2017
Date Written: May 16, 2013
In this paper we study asset demands and consumption of an individual at the end of her life cycle. We present an ideal market where complete insurance against longevity risk is available: the market consists of original assets, e.g., stocks and bonds, and annuities and life-insurance contracts linked to these assets. We also study asset demand and consumption for the other two cases: the no insurance case where there is no insurance available against longevity risk, and the partial insurance case where only bond-linked annuities exist for longevity insurance. We express asset demands in each case by using state price densities, and the expressions admit intuitive explanations. We derive consumption in analytic form and conduct comparative statics. Afterwards, we extend the model to multiple periods and show results of numerical simulation.
We find the proportion of wealth invested in risky assets to total savings in the complete market case is similar to the proportion in the no insurance case. It is, however, in general larger in the complete market case than in the partial insurance case. Under reasonable conditions the optimal consumption to wealth ratio is the highest in the complete insurance market, followed by the ratio in the partial insurance case, and the smallest in the no insurance case. Furthermore, simulation results show that asset demands can change quite dramatically as the prices of annuity products change. Thus, innovations in the insurance industry which lower costs of providing personalized insurance may result in a significant shift in asset demands, particularly in the demand for risky assets.
We also show that the time-old proposition that an increased mortality rate is equivalent to an increased subjective discount rate does not necessarily follow if we relax the assumption of the time-separable utility function. For a fixed relative risk aversion coefficient, comparative statics of optimal consumption yield different results depending on whether the EIS is greater or less than 1.
Keywords: longevity risk, asset demand, consumption, life insurance, annuity
JEL Classification: E21, G11, G22
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