Optimal allocation of policy deductibles for exchangeable risks

Sirous Fathi Manesh, Baha-Eldin Khaledi and Jan Dhaene

Insurance: Mathematics and Economics, 2016, vol. 71, issue C, 87-92

Abstract: Let X1,…,Xn be a set of n continuous and non-negative random variables, with log-concave joint density function f, faced by a person who seeks for an optimal deductible coverage for these n risks. Let d=(d1,…dn) and d∗=(d1∗,…dn∗) be two vectors of deductibles such that d∗ is majorized by d. It is shown that ∑i=1n(Xi∧di∗) is larger than ∑i=1n(Xi∧di) in stochastic dominance, provided f is exchangeable. As a result, the vector (∑i=1ndi,0,…,0) is an optimal allocation that maximizes the expected utility of the policyholder’s wealth. It is proven that the same result remains to hold in some situations if we drop the assumption that f is log-concave.

Keywords: Hazard rate order; Increasing convex order; Likelihood ratio order; Log-concave density function; Majorization; Schur-concave function; Stochastic dominance (search for similar items in EconPapers)
Date: 2016
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Citations: View citations in EconPapers (2)

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Working Paper: Optimal allocation of policy deductibles for exchangeable risks (2015)
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Persistent link: https://EconPapers.repec.org/RePEc:eee:insuma:v:71:y:2016:i:c:p:87-92

DOI: 10.1016/j.insmatheco.2016.07.010

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