Abstract
| Original language | English |
|---|---|
| Pages (from-to) | 107-121 |
| Journal | Insurance: Mathematics and Economics |
| Volume | 72 |
| DOIs | |
| Publication status | Published - Jan 2017 |
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Keywords
- optimal consumption
- portfolio selection
- longevity risk
- CIR process
- laplace transform
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Existence of optimal consumption strategies in markets with longevity risk. / de Kort, Jan; Vellekoop, M.H.
In: Insurance: Mathematics and Economics, Vol. 72, 01.2017, p. 107-121.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 -