### Abstract

Original language | English |
---|---|

Pages (from-to) | 107-121 |

Journal | Insurance: Mathematics and Economics |

Volume | 72 |

DOIs | |

Publication status | Published - Jan 2017 |

### Fingerprint

### Keywords

- optimal consumption
- portfolio selection
- longevity risk
- CIR process
- laplace transform

### Cite this

*Insurance: Mathematics and Economics*,

*72*, 107-121. https://doi.org/10.1016/j.insmatheco.2016.10.013

}

*Insurance: Mathematics and Economics*, vol. 72, pp. 107-121. https://doi.org/10.1016/j.insmatheco.2016.10.013

**Existence of optimal consumption strategies in markets with longevity risk.** / de Kort, Jan; Vellekoop, M.H.

Research output: Contribution to journal › Article › Scientific › peer-review

TY - JOUR

T1 - Existence of optimal consumption strategies in markets with longevity risk

AU - de Kort, Jan

AU - Vellekoop, M.H.

PY - 2017/1

Y1 - 2017/1

N2 - Survival bonds are financial instruments with a payoff that depends on human mortality rates. In markets that contain such bonds, agents optimizing expected utility of consumption and terminal wealth can mitigate their longevity risk. To examine how this influences optimal portfolio strategies and consumption patterns, we define a model in which the death of the agent is represented by a single jump process with Cox–Ingersoll–Ross intensity. This implies that our stochastic mortality rate is guaranteed to be nonnegative, in contrast to many other models in the literature. We derive explicit conditions for existence of an optimal consumption and investment strategy in terms of model parameters by analysing certain inhomogeneous Riccati equations. We find that constraints must be imposed on the market price of longevity risk to have a well-posed problem and we derive the optimal strategies when such constraints are satisfied.

AB - Survival bonds are financial instruments with a payoff that depends on human mortality rates. In markets that contain such bonds, agents optimizing expected utility of consumption and terminal wealth can mitigate their longevity risk. To examine how this influences optimal portfolio strategies and consumption patterns, we define a model in which the death of the agent is represented by a single jump process with Cox–Ingersoll–Ross intensity. This implies that our stochastic mortality rate is guaranteed to be nonnegative, in contrast to many other models in the literature. We derive explicit conditions for existence of an optimal consumption and investment strategy in terms of model parameters by analysing certain inhomogeneous Riccati equations. We find that constraints must be imposed on the market price of longevity risk to have a well-posed problem and we derive the optimal strategies when such constraints are satisfied.

KW - optimal consumption

KW - portfolio selection

KW - longevity risk

KW - CIR process

KW - laplace transform

U2 - 10.1016/j.insmatheco.2016.10.013

DO - 10.1016/j.insmatheco.2016.10.013

M3 - Article

VL - 72

SP - 107

EP - 121

JO - Insurance: Mathematics & Economics

JF - Insurance: Mathematics & Economics

SN - 0167-6687

ER -