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Combining quota-share and excess of loss treaties on the reinsurance of n independent risks
Abstracts and Reviews
051025 (M52, B12, B13) Reinsurance of the risk of ruin (Rdassurance du risque de ruine). Ecole des Hautes Etudes Am&r M.H., Commerciales, Universit6 de Lausanne, 1015 Lausanne, Suisse, Bulletin of the Swiss Association of Actuaries, Vol. 91, nr. I, 1991, pp. 33-49. The paper proposes a reinsurance treaty, under which the reinsurer covers exclusively the risk of ruin of the insured. During the contractual period the reinsurer lends the necessary amount in the case of ruin. In the following this loan is adjusted dynamically to cover the deficit, and at the end of the period the reinsurer makes a payment (if necessary), so that the contingency reserve raises to its initial level. (A. Gisler) Keywords: Pension Plans, Stability.
051026 (M52, M.30, Mll, B92) On excess of loss reinsurance with reinstatements. Sundt B., The Wyatt Company A.S., P.O. Box 1508 Vika, 0117 Oslo, Norway, Bulletin of the Swiss Association of Actuaries, Vol. 91, nr. 1, 1991, pp. 51-66. This paper discusses calculation of premiums for excess of loss reinsurance with reinstatements. Both pure premiums and premiums loaded by the standard deviation principle are considered. With paid reinstatements the premium income can be considered as random, and therefore one cannot immediately apply the standard deviation principle in the usual way. Premium calculation when the aggregate claim is generated by a compound distribution is discussed, and a numerical example is given. (A. Gisler) Excess of Loss Reinsurance, Keywords: Reinstatements, Premium Calculation.
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contract with the existing book, the standard deviation of the contract, the standard deviation of the existing book, the acceptable probability of “ruin” of the company, and the yield required on marginal surplus (the additional surplus required for this contract). A new term is defined, the reluctance to write risk, and relatively simple formulas result for it and the premium, which satisfy intuitive reasonableness criteria. Extensions to include expenses and an existing “bank” are discussed, and application is made to the interesting case of excess layer pricing. Empirical comparison suggests that the market pricing is consistent with this approach. (Author) Keywords: Marginal Surplus, Reinsurance, Risk Load. 051028 (MS2)
Combining quota-share and excess of loss treaties on the reinsurance of n independent risks. Centeno de LOurdes, M., Simoes O., ISEG, Universidade T6cnica de Lisboa, Portugal, Astin Bulletin, Vol. 21, nr. 1, 1991. pp. 56-71. In this paper, the authors seek to find the optimal retentions for an insurance company which intends to reinsure each of n risks belonging to its portfolio, by means of a pure quota-share treaty, a pure excess of loss treaty or any combination of the two. The criterion chosen to the selection of the optimal programme is the maximization of the adjustment coefficient, attending to the relationship existing between this coefficient and Lundberg’s upper bound of the ruin probability. (Authors) Keywords: Optimal Retention, Adjustment Coeficient.
M54:
CATASTROPHIC RISKS
051027 (M52,B90) Reinsurer risk loads from marginal surplus requirements. Kreps R., Proceedings of the Casualty Actuarial
051029 (M54, B52) Climatic change: effects on natural catastrophes, economy and insurance industry. (Klimailndenmg:
Society, Vol. LXXVU, 1990, pp. 196-203. The return on the marginal surplus committed to support the variability of a proposed reinsurance contract is used to derive an appropriate risk load for reinsurers. The risk load is a linear combination of the standard deviation and variance of the return on the contract, and depends upon the covariance of the
Auswirkungen auf Naturkatastrophen, volkswirtschaft und Versicherung) Berx G., Munich, Germany, Zeitschrift fi@ die gesamte Versicherungswissenscha~, Vol. 79, 1990, pp. 81-93. There is an increasing amount of evidence that the cumulation of natural catastrophes might also be
051025 (M52, B12, B13) Reinsurance of the risk of ruin (Rdassurance du risque de ruine). Ecole des Hautes Etudes Am&r M.H., Commerciales, Universit6 de Lausanne, 1015 Lausanne, Suisse, Bulletin of the Swiss Association of Actuaries, Vol. 91, nr. I, 1991, pp. 33-49. The paper proposes a reinsurance treaty, under which the reinsurer covers exclusively the risk of ruin of the insured. During the contractual period the reinsurer lends the necessary amount in the case of ruin. In the following this loan is adjusted dynamically to cover the deficit, and at the end of the period the reinsurer makes a payment (if necessary), so that the contingency reserve raises to its initial level. (A. Gisler) Keywords: Pension Plans, Stability.
051026 (M52, M.30, Mll, B92) On excess of loss reinsurance with reinstatements. Sundt B., The Wyatt Company A.S., P.O. Box 1508 Vika, 0117 Oslo, Norway, Bulletin of the Swiss Association of Actuaries, Vol. 91, nr. 1, 1991, pp. 51-66. This paper discusses calculation of premiums for excess of loss reinsurance with reinstatements. Both pure premiums and premiums loaded by the standard deviation principle are considered. With paid reinstatements the premium income can be considered as random, and therefore one cannot immediately apply the standard deviation principle in the usual way. Premium calculation when the aggregate claim is generated by a compound distribution is discussed, and a numerical example is given. (A. Gisler) Excess of Loss Reinsurance, Keywords: Reinstatements, Premium Calculation.
13
contract with the existing book, the standard deviation of the contract, the standard deviation of the existing book, the acceptable probability of “ruin” of the company, and the yield required on marginal surplus (the additional surplus required for this contract). A new term is defined, the reluctance to write risk, and relatively simple formulas result for it and the premium, which satisfy intuitive reasonableness criteria. Extensions to include expenses and an existing “bank” are discussed, and application is made to the interesting case of excess layer pricing. Empirical comparison suggests that the market pricing is consistent with this approach. (Author) Keywords: Marginal Surplus, Reinsurance, Risk Load. 051028 (MS2)
Combining quota-share and excess of loss treaties on the reinsurance of n independent risks. Centeno de LOurdes, M., Simoes O., ISEG, Universidade T6cnica de Lisboa, Portugal, Astin Bulletin, Vol. 21, nr. 1, 1991. pp. 56-71. In this paper, the authors seek to find the optimal retentions for an insurance company which intends to reinsure each of n risks belonging to its portfolio, by means of a pure quota-share treaty, a pure excess of loss treaty or any combination of the two. The criterion chosen to the selection of the optimal programme is the maximization of the adjustment coefficient, attending to the relationship existing between this coefficient and Lundberg’s upper bound of the ruin probability. (Authors) Keywords: Optimal Retention, Adjustment Coeficient.
M54:
CATASTROPHIC RISKS
051027 (M52,B90) Reinsurer risk loads from marginal surplus requirements. Kreps R., Proceedings of the Casualty Actuarial
051029 (M54, B52) Climatic change: effects on natural catastrophes, economy and insurance industry. (Klimailndenmg:
Society, Vol. LXXVU, 1990, pp. 196-203. The return on the marginal surplus committed to support the variability of a proposed reinsurance contract is used to derive an appropriate risk load for reinsurers. The risk load is a linear combination of the standard deviation and variance of the return on the contract, and depends upon the covariance of the
Auswirkungen auf Naturkatastrophen, volkswirtschaft und Versicherung) Berx G., Munich, Germany, Zeitschrift fi@ die gesamte Versicherungswissenscha~, Vol. 79, 1990, pp. 81-93. There is an increasing amount of evidence that the cumulation of natural catastrophes might also be