Vigilant Measures of Risk and the Demand for Contingent Claims

Mario Ghossoub

Discussion Papers from Northwestern University, Center for Mathematical Studies in Economics and Management Science

Abstract: I examine a class of utility maximization problems with a not necessarily law-invariant 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.

Keywords: Contingent Claims; Heterogeneous Beliefs; Choquet Integral; Vigilance; Monotone Likelihood Ratio JEL Classification Numbers: C02; D81; D89; G11 (search for similar items in EconPapers)
Date: 2012-10-22
New Economics Papers: this item is included in nep-rmg and nep-upt
References: Add references at CitEc
Citations: View citations in EconPapers (2)

Downloads: (external link)
http://www.kellogg.northwestern.edu/research/math/papers/1555.pdf main text (application/pdf)
Our link check indicates that this URL is bad, the error code is: 404 Not Found (http://www.kellogg.northwestern.edu/research/math/papers/1555.pdf [301 Moved Permanently]--> https://www.kellogg.northwestern.edu/research/math/papers/1555.pdf)

Related works:
Journal Article: Vigilant measures of risk and the demand for contingent claims (2015)
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:nwu:cmsems:1555

Ordering information: This working paper can be ordered from

Access Statistics for this paper

More papers in Discussion Papers from Northwestern University, Center for Mathematical Studies in Economics and Management Science Center for Mathematical Studies in Economics and Management Science, Northwestern University, 580 Jacobs Center, 2001 Sheridan Road, Evanston, IL 60208-2014. Contact information at EDIRC.
Bibliographic data for series maintained by Fran Walker ( this e-mail address is bad, please contact ).