Vigilant measures of risk and the demand for contingent claims

Mario Ghossoub

Insurance: Mathematics and Economics, 2015, vol. 61, issue C, 27-35

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.

Keywords: Utility maximization; Optimal insurance design; Choquet integral; Distorted probabilities; Monotone Likelihood Ratio (search for similar items in EconPapers)
JEL-codes: C02 D89 G11 (search for similar items in EconPapers)
Date: 2015
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Citations: View citations in EconPapers (3)

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Related works:
Working Paper: Vigilant Measures of Risk and the Demand for Contingent Claims (2012)
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Persistent link: https://EconPapers.repec.org/RePEc:eee:insuma:v:61:y:2015:i:c:p:27-35

DOI: 10.1016/j.insmatheco.2014.11.009

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