An optimal co-reinsurance strategy

Najafabadi, Amir T. Payandeh; Bazaz, Ali Panahi

doi:10.1016/j.insmatheco.2016.04.005

Cited by 1 publication

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“…The Bayesian method under name of the credibility method is well-known in various areas of the actuarial sciences. For instance see: Whitney (1918) and Payandeh Najafabadi & Qazvini (2015) for its application in the experience rating system; Bailey (1950), Payandeh Najafabadi (2010) and Payandeh Najafabadi et al . (2012) for its application in evaluating insurance premium; Hesselager & Witting (1988) and England & Verrall (2002) for its application in the IBNR claims reserving system; and see Makov et al .…”

Section: Simulation Studymentioning

confidence: 99%

An optimal multi-layer reinsurance policy under conditional tail expectation

Najafabadi

Bazaz

2017

Ann. actuar. sci.

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A usual reinsurance policy for insurance companies admits one or two layers of the payment deductions. Under optimal criterion of minimizing the conditional tail expectation (CTE) risk measure of the insurer's total risk, this article generalized an optimal stop-loss reinsurance policy to an optimal multi-layer reinsurance policy. To achieve such optimal multi-layer reinsurance policy, this article starts from a given optimal stop-loss reinsurance policy f (·). In the first step, it cuts down an interval [0, ∞) into two intervals [0, M 1 ) and [M 1 , ∞). By shifting the origin of Cartesian coordinate system to (M 1 , f (M 1 )), and showing that under the CT E criteriais, again, an optimal policy. This extension procedure can be repeated to obtain an optimal k-layer reinsurance policy. Finally, unknown parameters of the optimal multi-layer reinsurance policy are estimated using some additional appropriate criteria. Three simulation-based studies have been conducted to demonstrate: (1) The practical applications of our findings and (2) How one may employ other appropriate criteria to estimate unknown parameters of an optimal multi-layer contract. The multi-layer reinsurance policy, similar to the original stop-loss reinsurance policy is optimal, in a same sense. Moreover it has some other optimal criteria which the original policy does not have. Under optimal criterion of minimizing general translative and monotone risk measure ρ(·) of either the insurer's total risk or both the insurer's and the reinsurer's total risks, this article (in its discussion) also extends a given optimal reinsurance contract f (·) to a multi-layer and continuous reinsurance policy.

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