Hostname: page-component-cd9895bd7-dk4vv Total loading time: 0 Render date: 2024-12-23T19:08:55.281Z Has data issue: false hasContentIssue false
  • English
  • Français

Optimal Reinsurance for Variance Related Premium Calculation Principles1

Published online by Cambridge University Press:  09 August 2013

Manuel Guerra  and
Maria de Lourdes Centeno
Manuel Guerra
Affiliation:
CEOC and ISEG -T.U.Lisbon, R. Quelhas 6, 1200-781 Lisboa, Portugal, E-mail: [email protected]
Maria de Lourdes Centeno
Affiliation:
CEMAPRE, ISEG -T.U.Lisbon, R. Quelhas 6, 1200-781 Lisboa, Portugal, E-mail: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

This paper deals with numerical computation of the optimal form of reinsurance from the ceding company point of view, when the cedent seeks to maximize the adjustment coefficient of the retained risk and the reinsurance loading is an increasing function of the variance.

We compare the optimal treaty with the best stop loss policy. The optimal arrangement can provide a significant improvement in the adjustment coefficient when compared to the best stop loss treaty. Further, it is substantially more robust with respect to choice of the retention level than stop-loss treaties.

Keywords

Adjustment coefficientoptimal reinsurancestop lossstandard deviation premium principlevariance premium principle
Type
Research Article
Information
ASTIN Bulletin: The Journal of the IAA , Volume 40 , Issue 1 , May 2010 , pp. 97 - 121
Copyright
Copyright © International Actuarial Association 2010

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Footnotes

1

This research has been supported by Fundação para a Ciência e a Tecnologia (FCT) – project PTDC/ECO/66693/2006 – through PIDDAC, partially funded by the Portuguese State Budget.

References

Arrow, K.J. (1963) Uncertainty and the Welfare of Medical Care. The American Economic Review, LIII, 941–973.Google Scholar
Borch, K. (1960) An Attempt to Determine the Optimum Amount of Stop Loss Reinsurance. Transactions of the 16th International Congress of Actuaries, 597–610.Google Scholar
Deprez, O. and Gerber, H.U. (1985) On convex principles of premium calculation. Insurance: Mathematics and Economics, 4, 179–189.Google Scholar
Guerra, M. and Centeno, M.L. (2008) Optimal Reinsurance policy: the adjustment coefficient and the expected utility criteria. Insurance Mathematics and Economis, 42, 529–539.CrossRefGoogle Scholar
Hesselager, O. (1990) Some results on optimal reinsurance in terms of the adjustment coefficient. Scandinavian Actuarial Journal, 1, 80–95.CrossRefGoogle Scholar
Kaluszka, M. (2004) An extension of Arrow's result on optimality of a stop loss contract. Insurance: Mathematics and Economics, 35, 524–536.Google Scholar
Quarteroni, A., Sacco, R. and Saleri, F. (2000) Numerical Mathematics. Springer-Verlag, New York.Google Scholar