Consumption-Investment Problems with Stochastic Mortality Risk

SAFE Working Paper No. 43

56 Pages Posted: 6 Mar 2014

Date Written: March 3, 2014


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.

Keywords: Stochastic mortality risk, Health jumps, Labor income risk, Portfolio choice, Insurance

JEL Classification: D91, G11

Suggested Citation

Schendel, Lorenz, Consumption-Investment Problems with Stochastic Mortality Risk (March 3, 2014). SAFE Working Paper No. 43, Available at SSRN: or

Lorenz Schendel (Contact Author)

Goethe University Frankfurt ( email )

Grüneburgplatz 1
Frankfurt am Main, 60323

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