Subjective probability, confidence, and Bayesian updating

摘要

I define subjective probabilities for an ambiguity averse agent who is given an exogenous information set △ containing the true probability law on the state space S. The agent in my model evaluates every uncertain prospect via a mixture of the least favorable scenario in △ and her unique subjective belief p. This parametric utility structure is characterized by four standard axioms-order, continuity, monotonicity, and Independence-where the last two conditions are modified via the information set △. Any pair of preferences ≥ and ≥2 in my model can be compared in terms of confidence-the weights attached to the subjective beliefs p_1 and p_2, respectively. The corresponding behavioral condition extends Epstein's comparative ambiguity aversion that leaves some rankings ≥1 and ≥2 unrelated. Moreover, I relax the well-known dynamic consistency principle and characterize the Bayesian updating rule for the belief p conditional on any non-null event in S.