Allocations of policy limits and ordering relations for aggregate remaining claims

Sirous Fathi Manesh and Baha-Eldin Khaledi

Insurance: Mathematics and Economics, 2015, vol. 65, issue C, 9-14

Abstract: Let X1,…,Xn be a set of n risks, with decreasing joint density function f, faced by a policyholder who is insured for this n risks, with upper limit coverage for each risk. Let l=(l1,…ln) and l∗=(l1∗,…ln∗) be two vectors of policy limits such that l∗ is majorized by l. It is shown that ∑i=1n(Xi−li)+ is larger than ∑i=1n(Xi−li∗)+ according to stochastic dominance if f is exchangeable. It is also shown that ∑i=1n(Xi−l(i))+ is larger than ∑i=1n(Xi−l(i)∗)+ according to stochastic dominance if either f is a decreasing arrangement or X1,…,Xn are independent and ordered according to the reversed hazard rate ordering. We apply the new results to multivariate Pareto distribution.

Keywords: Arrangement decreasing; Exchangeable random variables; Hazard rate order; Likelihood ratio order; Majorization; Reversed hazard rate order; Schur concave function; Stochastic dominance (search for similar items in EconPapers)
Date: 2015
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Citations: View citations in EconPapers (2)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:insuma:v:65:y:2015:i:c:p:9-14

DOI: 10.1016/j.insmatheco.2015.08.003

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