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Optimal allocation of policy deductibles for exchangeable risks

Author

Listed:
  • Sirous Fathi Manesh
  • Baha-Eldin Khaledi
  • Jan Dhaene

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 this n risks. Let d = (d1; : : : dn) and d = (d 1; : : : d n) be two vectors of deductibles such that d is majorized by d. It is shown that Σn i=1(Xi ^ di) is larger than Σn i=1(Xi ^ d i ) in stochastic dominance, provided f is exchangeable. As a result, the vector ( Σn i=1 di; 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

  • Sirous Fathi Manesh & Baha-Eldin Khaledi & Jan Dhaene, 2015. "Optimal allocation of policy deductibles for exchangeable risks," Working Papers Department of Accountancy, Finance and Insurance (AFI), Leuven 501184, KU Leuven, Faculty of Economics and Business (FEB), Department of Accountancy, Finance and Insurance (AFI), Leuven.
    • Handle: RePEc:ete:afiper:501184
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    2. Albrecht, Peter & Huggenberger, Markus, 2017. "The fundamental theorem of mutual insurance," Insurance: Mathematics and Economics, Elsevier, vol. 75(C), pages 180-188.
    3. Wei Wei, 2018. "Properties of Stochastic Arrangement Increasing and Their Applications in Allocation Problems," Risks, MDPI, vol. 6(2), pages 1-12, April.

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