Vigilant measures of risk and the demand for contingent claims

Arbeitspapier

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.

Object Details

• Language: Englisch

References and Relationships

• Bibliographic citation: Series: Discussion Paper ; No. 1555

Classification and Topics

• Classification: Wirtschaft ; Mathematical Methods ; Criteria for Decision-Making under Risk and Uncertainty ; Information and Uncertainty: Other ; Portfolio Choice; Investment Decisions
• Subject: Contingent Claims ; Heterogeneous Beliefs ; Choquet Integral ; Vigilance ; Monotone Likelihood Ratio ; Contingent Claims ; Heterogeneous Beliefs ; Choquet Integral ; Vigilance ; Monotone Likelihood Ratio

Contributors, Places and Time

• Event: Geistige Schöpfung
• (who): Ghossoub, Mario
• Event: Veröffentlichung
• (who): Northwestern University, Kellogg School of Management, Center for Mathematical Studies in Economics and Management Science
• (where): Evanston, IL
• (when): 2012

Further information

• Handle: http://hdl.handle.net/10419/97248
• Last update: 10.03.2025, 11:44 AM CET