论文标题
死亡率和医疗保健：Epstein-Zin偏好下的随机控制分析
Mortality and Healthcare: a Stochastic Control Analysis under Epstein-Zin Preferences
论文作者
论文摘要
本文研究了爱泼斯坦Zin偏好的最佳消费，投资和医疗支出。鉴于消费和医疗保健支出计划，爱泼斯坦 - 锌公用事业是在代理人的随机寿命上定义的，由于医疗保健降低了死亡率的增长，因此代理人可以部分控制。据我们所知，这是第一次通过无限 - 马的后向随机微分方程和超级线性生长的无限 - 马Zon向后的随机范围配制Epstein-Zin实用程序。为关联的效用价值过程的唯一性建立了一个新的比较结果。在黑色choles市场中，随机控制问题通过相关的汉密尔顿 - 雅各比 - 贝尔曼（HJB）方程解决。验证论点具有对控制道德过程的增长的微妙遏制，这是我们框架所独有的，依赖于概率论证和对HJB方程的分析的结合。与在时间分离的公用事业下先前的工作相反，爱泼斯坦 - Zin的偏好有助于校准。模型生成的死亡率紧密近似于美国和英国的实际死亡率数据；此外，可以在两国之间校准和比较医疗保健的功效。
This paper studies optimal consumption, investment, and healthcare spending under Epstein-Zin preferences. Given consumption and healthcare spending plans, Epstein-Zin utilities are defined over an agent's random lifetime, partially controllable by the agent as healthcare reduces mortality growth. To the best of our knowledge, this is the first time Epstein-Zin utilities are formulated on a controllable random horizon, via an infinite-horizon backward stochastic differential equation with superlinear growth. A new comparison result is established for the uniqueness of associated utility value processes. In a Black-Scholes market, the stochastic control problem is solved through the related Hamilton-Jacobi-Bellman (HJB) equation. The verification argument features a delicate containment of the growth of the controlled morality process, which is unique to our framework, relying on a combination of probabilistic arguments and analysis of the HJB equation. In contrast to prior work under time-separable utilities, Epstein-Zin preferences facilitate calibration. The model-generated mortality closely approximates actual mortality data in the US and UK; moreover, the efficacy of healthcare can be calibrated and compared between the two countries.
