死亡率与卫生保健：Epstein-Zin偏好下的随机控制分析
Mortality and Healthcare: a Stochastic Control Analysis under Epstein-Zin Preferences
摘要：
本文研究了Epstein-Zin偏好下的最优消费、投资和医疗支出。给定消费和医疗支出计划，Epstein-Zin效用在代理的随机生命周期内定义，部分可由代理控制，因为医疗保健降低了死亡率增长。据我们所知，这是第一次的Epstein-Zin效用制定一个可控的随机地平线上，通过一个无限地平线倒向随机微分方程超线性增长。对相关效用值过程的唯一性建立了一个新的比较结果。在Black-Scholes市场中，随机控制问题通过相关的Hamilton-Jacobi-Bellman（HJB）方程求解。验证论证的特点是对受控道德过程的增长进行了微妙的遏制，这是我们框架所独有的，它依赖于概率论证和对哈密顿-雅可比-贝尔曼方程的分析。与之前在时间可分离效用下的工作相比，爱泼斯坦-津偏好便于校准。模型生成的死亡率非常接近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。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
