Please use this identifier to cite or link to this item: http://hdl.handle.net/10419/97248
Authors: 
Ghossoub, Mario
Year of Publication: 
2012
Series/Report no.: 
Discussion Paper, Center for Mathematical Studies in Economics and Management Science 1555
Abstract: 
I examine a class of utility maximization problems with a not necessarily lawinvariant utility, and with a not necessarily law-invariant risk measure constraint. The objective function is an integral of some function U with respect to some probability measure P, and the constraint set contains some 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 given underlying random variable X and of a contingent claim Y on X. Many problems in economic theory and financial theory can be formulated in this manner, when a heterogeneity in the perception of uncertainty is introduced. Under a consistency requirement on the risk measure that will be called Vigilance, supermodularity of the primitive U is sufficient for the existence of optimal continent claims, and for these optimal claims to be comonotonic with the underlying random variable X. Vigilance is satisfied by a large class of risk measures, including all distortion risk measures. An explicit characterization of an optimal contingent claim is also provided in the case where the risk measure is a convex distortion risk measure.
Subjects: 
Contingent Claims
Heterogeneous Beliefs
Choquet Integral
Vigilance
Monotone Likelihood Ratio
Contingent Claims
Heterogeneous Beliefs
Choquet Integral
Vigilance
Monotone Likelihood Ratio
JEL: 
C02
D81
D89
G11
Document Type: 
Working Paper

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