On the Recoverability of Preferences and Beliefs
研究能否从投资者的消费选择中同时恢复其偏好和信念，发现通过一个鞅条件可刻画所有一致的效用函数和信念，且在马尔可夫情形下可转化为黎卡提微分方程，并证明在特定效用函数类中偏好和信念可唯一恢复。
We examine the extent to which an investor's tastes and beliefs can be jointly recovered from knowledge of his/her consumption choice. More precisely, we assume that the investor's preferences admit an expected utility representation, but with subjective (unknown) probabilities, and investigate what joint restrictions can be placed on utility functions and beliefs. If the investor draws utility from intertemporal consumption, we show that the set of utility functions and beliefs that are consistent with a given consumption choice can be characterized by a martingale condition. In the Markovian case, this characterization can be restated in terms of a Riccati differential equation that must be satisfied by the investor's relative risk aversion function. To each solution of this differential equation is associated a unique utility function and a unique set of beliefs supporting the given consumption choice. Moreover, we show that the differential equation has at most one solution in the class of utility functions displaying infinite absolute risk aversion at the origin. Thus, preferences (and associated beliefs) can be uniquely recovered within this class.