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Optimal allocation of policy deductibles for exchangeable risks

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  • Manesh, Sirous Fathi
  • Khaledi, Baha-Eldin
  • Dhaene, Jan

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.

Suggested Citation

  • Manesh, Sirous Fathi & Khaledi, Baha-Eldin & Dhaene, Jan, 2016. "Optimal allocation of policy deductibles for exchangeable risks," Insurance: Mathematics and Economics, Elsevier, vol. 71(C), pages 87-92.
    • Handle: RePEc:eee:insuma:v:71:y:2016:i:c:p:87-92
    DOI: 10.1016/j.insmatheco.2016.07.010
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    References listed on IDEAS

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