Journal article
Vigilant measures of risk and the demand for contingent claims
Insurance, mathematics & economics, Vol.61, pp.27-35
03/01/2015
DOI: 10.1016/j.insmatheco.2014.11.009
Abstract
We examine a class of utility maximization problems with a non-necessarily law-invariant utility, and with a non-necessarily law-invariant risk measure constraint. Under a consistency requirement on the risk measure that we call Vigilance, we show the existence of optimal contingent claims, and we show that such optimal contingent claims exhibit a desired monotonicity property. Vigilance is satisfied by a large class of risk measures, including all distortion risk measures and some classes of robust risk measures. As an illustration, we consider a problem of optimal insurance design where the premium principle satisfies the vigilance property, hence covering a large collection of commonly used premium principles, including premium principles that are not law-invariant. We show the existence of optimal indemnity schedules, and we show that optimal indemnity schedules are nondecreasing functions of the insurable loss.
Details
- Title: Subtitle
- Vigilant measures of risk and the demand for contingent claims
- Creators
- Mario Ghossoub - Imperial College London
- Resource Type
- Journal article
- Publication Details
- Insurance, mathematics & economics, Vol.61, pp.27-35
- DOI
- 10.1016/j.insmatheco.2014.11.009
- ISSN
- 0167-6687
- eISSN
- 1873-5959
- Publisher
- Elsevier B.V
- Number of pages
- 9
- Language
- English
- Date published
- 03/01/2015
- Academic Unit
- Statistics and Actuarial Science
- Record Identifier
- 9985179850202771
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