Living With Ambiguity: Pricing Mortality‐Linked Securities With Smooth Ambiguity Preferences
研究了模糊性和模糊厌恶对死亡率关联证券价格的影响，比较了无参数不确定性、贝叶斯更新和平滑模糊偏好三种情景下的定价差异，发现模糊厌恶的影响远小于风险厌恶。
A BSTRACT Mortality is a stochastic process. We have imprecise knowledge about the probability distribution of mortality rates in the future. Mortality risk, therefore, can be defined in a broader term of ambiguity. In this article, we investigate the effects of ambiguity and ambiguity aversion on prices of mortality‐linked securities. Ambiguity may arise from parameter uncertainty due to a finite sample of data and inaccurate old‐age mortality rates. We compare the price of a mortality bond in three scenarios: (1) no parameter uncertainty, (2) parameter uncertainty with Bayesian updates, and (3) parameter uncertainty with the smooth ambiguity preference. We use the indifference pricing approach to derive the minimum ask price and the maximum bid price, and adopt the economic pricing method to compute the equilibrium price that clears the market. We reveal the connection between the indifference pricing approach and the economic pricing approach and find that ambiguity aversion has a much smaller effect on prices of mortality‐linked securities than risk aversion in our example.