Mortality Contingent Claims: Impact of Capital Market, Income, and Interest Rate Risk

Published: 2009


In this paper, we consider optimal insurance, portfolio allocation, and consumption rules for a stochastic wage earner with CRRA preferences whose lifetime is random. In a continuous time framework, the investor has to decide among short and long positions in mortality contingent claims a.k.a. life insurance, stocks, bonds, and money market investment when facing a risky stock market and interest rate risk. We find an analytical solution for the complete market case in which human capital is exactly priced. We also extend the analysis to the case where income is unspanned. An illustrative analysis shows when the wage earner’s demand for life insurance switches to the demand for annuities.

Key Findings

    • We explore how an investor can accumulate wealth and manage her assets effectively to meet the consumption and bequest liabilities that arise during her lifetime using pension annuities and life insurance policies with guaranteed payouts.
    • We find a substantial impact of financial wealth with respect to the demand for life insurance policies, but we discover a considerably small influence of the short rate on the demand for life insurance if we reasonably calibrate our asset and income model.
    • We find an analytical solution for the optimal demand for life insurance and pension annuities in the complete market case in which human capital is exactly priced, and derive numerical insight into a realistically calibrated case when uncertain income is unspanned.