Date: Thursday, February 16, 2012
Location: 1360 East Hall (3:00 PM to 4:00 PM)
Title: On a Class of Monotone Comparative Statics Problems under Heterogeneous Uncertainty, with an Application to Insurance.
Abstract: We examine a class of monotone comparative statics problems under uncertainty that arise naturally in many areas of economic theory, but that cannot be solved directly using the classical Topkis-Milgrom-Shannon-Athey techniques. The objective function is an aggregation of some function U with respect to some probability measure P, and the constraint set contains some "aggregation constraint" (e.g. a risk measure constraint) which is not necessarily P-law-invariant. This introduces some heterogeneity in the perception of uncertainty. The primitive U is a function of some underlying random variable X and of a contingent claim Y on X. The choice variable is Y, and conditions on the primitive U and the "aggregation constraint" so that the problem admits a solution which is a nondecreasing function of X are desired. Under a consistency requirement on the "aggregation constraint" that will be called "Vigilance", supermodularity of the primitive U is sufficient for monotone comparative statics to hold. It is shown that in most situations, the assumption of Vigilance is (strictly) weaker than the usual assumption of a Monotone Likelihood Ratio, when the latter can be defined. As an application, we extend the Arrow-Borch-Raviv classical model of demand for insurance contracts to situations of heterogeneous beliefs, and show that an optimal indemnity schedule for the insurance buyer takes the shape of what we call a "generalized deductible contract". Moreover, the class of all optimal insurance contracts for the insurance buyer that are nondecreasing in the loss is fully characterized in terms of their distribution for the insurance buyer.
Speaker: Mario Ghossoub
Institution: University of Montreal
Event Organizer: Erhan Bayraktar erhan@umich.edu
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