Existence of optimal consumption strategies in markets with longevity risk

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• 作者：J. de Kort ; ^{j.dekort@uva.nl} ; M.H. Vellekoop ^{m.h.vellekoop@uva.nl}
• 关键词：Optimal consumption ; Portfolio selection ; Longevity risk ; CIR process ; Laplace transform
• 刊名：Insurance: Mathematics and Economics
• 出版年：2017
• 出版时间：January 2017
• 年：2017
• 卷：72
• 期：Complete
• 页码：107-121
• 全文大小：611 K
• 卷排序：72

文摘

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.