Optimal Dynamic Consumption and Portfolio Choice for Pooled Annuity Funds
Optimal Dynamic Consumption and Portfolio Choice for Pooled Annuity Funds
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DOI：
10.2139/ssrn.971727
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发表时间：
2007-04
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影响因子：
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通讯作者：
Michael Stamos
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文献类型：
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作者：
Michael Stamos
研究了集合型年金基金的最优连续时间动态消费与投资组合问题。与购买终身年金相比，集合年金基金是防范死亡风险的另一种方式。汇集年金基金与购买保险公司提供的终身年金之间的关键区别在于，汇集年金基金的参与者仍然需要承担一些死亡风险，而投保年金则完全没有死亡风险。人口的池建模采用泊松过程与时间相关的风险率。由此可见，池成员的优化问题必须考虑到随机的投资范围，以及如果另一个池成员死亡而发生的财富跳跃。如果池成员的数量达到无穷大，则提供分析解决方案。对于有限的池大小的优化问题的解决方案减少到一组常微分方程的数值解。一个模拟和福利分析表明，汇集年金基金非常有效地防止长寿风险，即使他们的游泳池规模相当小。只有非常厌恶风险的投资者或那些无法进入小型资金池的投资者才更倾向于支付风险溢价进入私人人寿年金市场，以完全消除死亡风险。由于即使是家庭也构成了如此小的资金池，该模型为低经验年金需求提供了理论依据。
This paper presents the optimal continuous time dynamic consumption and portfolio choice for pooled annuity funds. A pooled annuity fund constitutes an alternative way to protect against mortality risk compared to purchasing a life annuity. The crucial difference between the pooled annuity fund and purchase of a life annuity offered by an insurance company is that participants of a pooled annuity fund still have to bear some mortality risk while insured annuitants bear no mortality risk at all. The population of the pool is modeled by employing a Poisson process with time-dependent hazard-rate. It follows that the pool member's optimization problem has to account for the stochastic investment horizon and for jumps in wealth which occur if another pool member dies. In case the number of pool members goes to infinity analytical solutions are provided. For finite pool sizes the solution of the optimization problem is reduced to the numerical solution of a set of ODEs. A simulation and welfare analysis show that pooled annuity funds insure very effectively against longevity risk even if their pool size is rather small. Only very risk averse investors or those without access to small pools are more inclined to pay a risk premium to access private life annuity markets in order to lay off mortality risk completely. As even families constitute such small pools the model provides theoretical justification for the low empirical annuity demand.