Consistency Issues in State-Dependent Preferences

In this talk, I will discuss how a family of conditional nonlinear expectations, satisfying a natural consistency property, collapses to a conditional certainty equivalent defined via a state-dependent utility function. This result is achieved by embedding the problem within a decision-theoretic framework and providing a novel characterization of the Sure-Thing Principle. Specifically, we show that this principle characterizes those preference relations that admit consistent backward conditional projections. In the second part of the talk, I will explore how an agent with exponential preferences and uncertain (random) risk aversion can attain time-consistent and horizon-independent strategies, provided that the agent filters her future risk aversion through a specific stochastic process. This talk is based on joint work with E. Berton and A. Doldi.