Optimal allocation of policy deductibles for exchangeable risks

Sirous Fathi Manesh, Baha-Eldin Khaledi and Jan Dhaene

No 501184, Working Papers Department of Accountancy, Finance and Insurance (AFI), Leuven from KU Leuven, Faculty of Economics and Business (FEB), Department of Accountancy, Finance and Insurance (AFI), Leuven

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.

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: 2015
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Published in FEB Research report AFI_15103 , pages 1-14

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Journal Article: Optimal allocation of policy deductibles for exchangeable risks (2016)
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