Existence of optimal consumption strategies in markets with longevity risk

Jan de Kort, M.H. Vellekoop

Research output: Contribution to journalArticleScientificpeer-review

Abstract

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.
Original languageEnglish
Pages (from-to)107-121
JournalInsurance: Mathematics and Economics
Volume72
DOIs
Publication statusPublished - Jan 2017

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Mortality Rate
Well-posed Problem
Jump Process
Optimal Portfolio
Expected Utility
Riccati Equation
Optimal Strategy
Non-negative
Model
Imply
Market
Strategy
Longevity risk
Optimal consumption
Mortality rate
Influence
Human
Expected utility
Portfolio strategy
Wealth

Keywords

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

Cite this

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title = "Existence of optimal consumption strategies in markets with longevity risk",
abstract = "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.",
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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 journalArticleScientificpeer-review

TY - JOUR

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

AU - de Kort, Jan

AU - Vellekoop, M.H.

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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

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