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Optimal reinsurance from the point of view of the excess of loss reinsurer under the finite-time ruin criterion
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Abstracts and Reviews
073033 (M52) Reduction of uncertainty through Actualization of intervals Possibilities and its application to reinsurance. Babad Y.M., Berliner B., Israel, Transactions 1CA Brussels, 1995, Vol. 2, pp. 23-36. Modeling the real world requires the expression and analysis of vague, fuzzy, and imprecise information. Probability theory and fuzzy set theory address this need within certain limitation, as do intervals of possibilities which require minimal amount of information about the uncertain values. One drawback of interval arithmetic and fuzzy sets is the possible increase in imprecision, as expressed by the width of the resulting intervals and fuzzy numbers. In this paper we demonstrate how to overcome this drawback, and improve the resulting precision through the consideration of actualization, which recognizes that once a value from an interval is selected, it must consistently be used wherever this interval is used. Actualization is then illustrated In matrix operations and stop-loss reinsurance. Keywords: Stop-Loss, Fuzzy Set. 073034 (M52) The Roll-over Stop-loss Method. An Alternative Experience Rating Technique For Collective Contracts. Cielen R., Belgium, Transactions 1CA Brussels, 1995, Vol. 2, pp. 61-92. Due to the ever increasing competition in the market of collective contracts, virtually all mid-sized and larger employers obtain from their insurer(s) considerable cost reduction in the form of local profit sharing formulas. These local dividends can be used either to decrease future premiums or to improve benefits insured. On top of such local dividends, many multinationals have set up one or more pools with one or several networks of insurance companies which enable them to benefit from refunds or dividends on the international level. These international dividends are the result of the experience rating of nation-wide employee benefits insurances in different countries. Be it local '(i.e., national) or international dividend formulas, both approaches to experience rating collective contracts need to be based on a solid method. This paper focuses on an alternative method to experience rate collective contracts nationally or internationally: i.e. the Roll-Over Stop-Loss method (ROSL). Any collective contract or group of collective contracts which has shown favorable claims experience may be
entitled to a refund. However, upon unfavorable claims experience, losses are carried forward individually and for maximum n consecutive times. Any loss still outstanding afterwards will be wiped out by a stop-loss protection and has to be borne by the insurer. Several approaches towards the calculation of a risk premium under a ROSL method have been presented, each of them being put in perspective with regard to the other, and as compared to some wide-spread experience rating techniques. Though they all generate different risk premiums, it is also shown that they nevertheless are actuarially equivalent. Keywords: Dividend, Stop-Loss. 073035 (M52) A Reassuring future? Daniel W., Huntley D., U.K., Transactions lCA Brussels, 1995, Vol.2, pp. 93-120. This paper has been written with the objective of provoking discussion and debate on the subject of the future strategic direction for the reinsurance industry. The paper takes a composite view of the industry and considers issues from a global perspective. The first section identifies and briefly discusses the key themes fuelling the current changes within the insurance sector. The second section examines the potential implications for the reinsurance industry that these changes will bring about and considers the possible strategic direction for reinsurance companies in the future as a result. Given the objective of the paper, there is no formal conclusion. However, the authors take the view that those reinsurers likely to be most successful, will be forward thinking companies with bold leadership and clear strategic vision. We also believe that the reinsurance industry will polarize into two distinct groupings: one being the large, well capitalised, global players; the other the smaller, local specialist reinsurers. Keywords: Reinsurers. 073036 (M52) Optimal reinsurance from the point of view of the excess of loss reinsurer under the finite-time ruin criterion. De Longueville P., Belgium, Transactions lCA Brussels, 1995, Vol. 2, pp. 121-140. Speaking about optimal reinsurance, we often think of an insurance company which tries to optimize its reinsurance program under a certain criterion. Among all possible criterions, the finite-time ruin probability is very recently introduced in actuarial literature. This
Abstracts and Reviews
criterion has two major advantages: it gives the possibility to measure the risk on a medium or short time-period, and it allows to compare reinsurance programs having the same total reinsurance premium, and thus the same cost. In this paper, we consider opt imal reinsurance from the point of view of the excess of loss (XL) reinsurer. We deduce how the finite-time ruin probability of a portfolio conserved by an XL reinsurer can be calculated. The finite-time ruin probability can then be used to optimally fix the priority and/or the limit of an XL treaty. In practice, XL reinsurance is often accompanied by annual clauses, such as aggregate deductible, slide premium, and reinstatements. These clauses have as effect to modify the XL premium and the repartition of the charge between insurer and XL reinsurer. On top this paper shows how these annual clauses can be introduced in the algorithm of calculation of the finite-time ruin probability. So, for fixed priority and limit, the reinsurer has a criterion to decide to introduce a clause, to compare a combination of clauses versus any other, or to fix the parameters of a clause, even if all the possibilities result in the same XL premium. He can finally choose the combination which minimizes the finite-time ruin probability of the conserved portfolio. Keywords: Excess of Loss.
073037 (M52) Links between premium principles and Reinsurance. Hiirlimann W., Switzerland, Transactions 1CA Brussels, 1995 Vol. 2, pp. 141-168. In order to analyze problems of decision-making in reinsurance (and option) markets, a general class of reinsurance oriented premium principles is introduced. Taking into account the economic value of a reinsurance program, this class shrinks to an interesting subclass of economic reinsurance based premium principles. Specific reinsurance programs may be further eliminated if they do not satisfy three plausible rules of consistency. The following topics illustrate how the considered concept leads to useful results of an obvious interest in Insurance and Finance: • The calculation of an adequate insurance premium, which fulfills a given one-year level of solvability. • The interpretation of the expected value principle and the distribution-free parameter-free modified variance principle as economic stop-loss reinsurance based premium principles.
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• The construction of an economic reinsurance based premium principle using an experience rated insurance contract, which besides claims payment guarantees a given claims dependent bonus payment. • The rational determination of a guaranteed return portfolio insurance can achieve. • The analysis of conditions under which a quota-share treaty leads to a reinsurance based premium principle. Keyw ords: Solvability, Reinsurance, Bonus.
073038 (M52) How to cope with wind storms. Simulation to search for the most efficient way to stabilize the insurance company management using a mix of reinsurance and reserve for catastrophe loss in Japan. Mayuzumi T., Japan, Transactions 1CA Brussels, 1995. Vol. 2, pp. 225-262 . Typhoon No. 19 of 1991 (MiIleile) compelled non-life insurance companies in Japan to pay huge amount of insurance claims. Therefore, it became an urgent issue for non-life insurance companies in Japan to make statistical analyses of catastrophic disasters such as typhoon and establish an appropriate protection method through an actuarial approach. The purpose of this paper is to consider what kind of influence is exerted by ELC reinsurance and the reserve for catastrophe loss (RCL) -which is unique to Japan- on losses caused by a typhoon which is assumed to take place at specific distribution, and as a result , to consider what is the most proper way for insurance companies to cope with it. More specifically I) I determined the distribution of losses caused by typhoons , based on the data of "monthly report issued" by Meteorological Agency for the last 25 years; 2) I simulated typhoon losses for 10,000 years based on the typhoon loss distribution determined in the above. 3) I determined the scale of the insurance company to be used as a model, paying due consideration to the average size of direct writing companies in Japan; 4) I determined the rule for appropriating and disposing the RCL, and assumed a plural pattern for RCL. I assumed 3 patterns for the RCL as folJows: • A pattern which has no RCL Pattern 0 • A pattern with which the appropriation rate of RCL is 2% Pattern 2 • A pattern with which the appropriation rate of RCL is ~
~~rn4
Abstracts and Reviews
073033 (M52) Reduction of uncertainty through Actualization of intervals Possibilities and its application to reinsurance. Babad Y.M., Berliner B., Israel, Transactions 1CA Brussels, 1995, Vol. 2, pp. 23-36. Modeling the real world requires the expression and analysis of vague, fuzzy, and imprecise information. Probability theory and fuzzy set theory address this need within certain limitation, as do intervals of possibilities which require minimal amount of information about the uncertain values. One drawback of interval arithmetic and fuzzy sets is the possible increase in imprecision, as expressed by the width of the resulting intervals and fuzzy numbers. In this paper we demonstrate how to overcome this drawback, and improve the resulting precision through the consideration of actualization, which recognizes that once a value from an interval is selected, it must consistently be used wherever this interval is used. Actualization is then illustrated In matrix operations and stop-loss reinsurance. Keywords: Stop-Loss, Fuzzy Set. 073034 (M52) The Roll-over Stop-loss Method. An Alternative Experience Rating Technique For Collective Contracts. Cielen R., Belgium, Transactions 1CA Brussels, 1995, Vol. 2, pp. 61-92. Due to the ever increasing competition in the market of collective contracts, virtually all mid-sized and larger employers obtain from their insurer(s) considerable cost reduction in the form of local profit sharing formulas. These local dividends can be used either to decrease future premiums or to improve benefits insured. On top of such local dividends, many multinationals have set up one or more pools with one or several networks of insurance companies which enable them to benefit from refunds or dividends on the international level. These international dividends are the result of the experience rating of nation-wide employee benefits insurances in different countries. Be it local '(i.e., national) or international dividend formulas, both approaches to experience rating collective contracts need to be based on a solid method. This paper focuses on an alternative method to experience rate collective contracts nationally or internationally: i.e. the Roll-Over Stop-Loss method (ROSL). Any collective contract or group of collective contracts which has shown favorable claims experience may be
entitled to a refund. However, upon unfavorable claims experience, losses are carried forward individually and for maximum n consecutive times. Any loss still outstanding afterwards will be wiped out by a stop-loss protection and has to be borne by the insurer. Several approaches towards the calculation of a risk premium under a ROSL method have been presented, each of them being put in perspective with regard to the other, and as compared to some wide-spread experience rating techniques. Though they all generate different risk premiums, it is also shown that they nevertheless are actuarially equivalent. Keywords: Dividend, Stop-Loss. 073035 (M52) A Reassuring future? Daniel W., Huntley D., U.K., Transactions lCA Brussels, 1995, Vol.2, pp. 93-120. This paper has been written with the objective of provoking discussion and debate on the subject of the future strategic direction for the reinsurance industry. The paper takes a composite view of the industry and considers issues from a global perspective. The first section identifies and briefly discusses the key themes fuelling the current changes within the insurance sector. The second section examines the potential implications for the reinsurance industry that these changes will bring about and considers the possible strategic direction for reinsurance companies in the future as a result. Given the objective of the paper, there is no formal conclusion. However, the authors take the view that those reinsurers likely to be most successful, will be forward thinking companies with bold leadership and clear strategic vision. We also believe that the reinsurance industry will polarize into two distinct groupings: one being the large, well capitalised, global players; the other the smaller, local specialist reinsurers. Keywords: Reinsurers. 073036 (M52) Optimal reinsurance from the point of view of the excess of loss reinsurer under the finite-time ruin criterion. De Longueville P., Belgium, Transactions lCA Brussels, 1995, Vol. 2, pp. 121-140. Speaking about optimal reinsurance, we often think of an insurance company which tries to optimize its reinsurance program under a certain criterion. Among all possible criterions, the finite-time ruin probability is very recently introduced in actuarial literature. This
Abstracts and Reviews
criterion has two major advantages: it gives the possibility to measure the risk on a medium or short time-period, and it allows to compare reinsurance programs having the same total reinsurance premium, and thus the same cost. In this paper, we consider opt imal reinsurance from the point of view of the excess of loss (XL) reinsurer. We deduce how the finite-time ruin probability of a portfolio conserved by an XL reinsurer can be calculated. The finite-time ruin probability can then be used to optimally fix the priority and/or the limit of an XL treaty. In practice, XL reinsurance is often accompanied by annual clauses, such as aggregate deductible, slide premium, and reinstatements. These clauses have as effect to modify the XL premium and the repartition of the charge between insurer and XL reinsurer. On top this paper shows how these annual clauses can be introduced in the algorithm of calculation of the finite-time ruin probability. So, for fixed priority and limit, the reinsurer has a criterion to decide to introduce a clause, to compare a combination of clauses versus any other, or to fix the parameters of a clause, even if all the possibilities result in the same XL premium. He can finally choose the combination which minimizes the finite-time ruin probability of the conserved portfolio. Keywords: Excess of Loss.
073037 (M52) Links between premium principles and Reinsurance. Hiirlimann W., Switzerland, Transactions 1CA Brussels, 1995 Vol. 2, pp. 141-168. In order to analyze problems of decision-making in reinsurance (and option) markets, a general class of reinsurance oriented premium principles is introduced. Taking into account the economic value of a reinsurance program, this class shrinks to an interesting subclass of economic reinsurance based premium principles. Specific reinsurance programs may be further eliminated if they do not satisfy three plausible rules of consistency. The following topics illustrate how the considered concept leads to useful results of an obvious interest in Insurance and Finance: • The calculation of an adequate insurance premium, which fulfills a given one-year level of solvability. • The interpretation of the expected value principle and the distribution-free parameter-free modified variance principle as economic stop-loss reinsurance based premium principles.
69
• The construction of an economic reinsurance based premium principle using an experience rated insurance contract, which besides claims payment guarantees a given claims dependent bonus payment. • The rational determination of a guaranteed return portfolio insurance can achieve. • The analysis of conditions under which a quota-share treaty leads to a reinsurance based premium principle. Keyw ords: Solvability, Reinsurance, Bonus.
073038 (M52) How to cope with wind storms. Simulation to search for the most efficient way to stabilize the insurance company management using a mix of reinsurance and reserve for catastrophe loss in Japan. Mayuzumi T., Japan, Transactions 1CA Brussels, 1995. Vol. 2, pp. 225-262 . Typhoon No. 19 of 1991 (MiIleile) compelled non-life insurance companies in Japan to pay huge amount of insurance claims. Therefore, it became an urgent issue for non-life insurance companies in Japan to make statistical analyses of catastrophic disasters such as typhoon and establish an appropriate protection method through an actuarial approach. The purpose of this paper is to consider what kind of influence is exerted by ELC reinsurance and the reserve for catastrophe loss (RCL) -which is unique to Japan- on losses caused by a typhoon which is assumed to take place at specific distribution, and as a result , to consider what is the most proper way for insurance companies to cope with it. More specifically I) I determined the distribution of losses caused by typhoons , based on the data of "monthly report issued" by Meteorological Agency for the last 25 years; 2) I simulated typhoon losses for 10,000 years based on the typhoon loss distribution determined in the above. 3) I determined the scale of the insurance company to be used as a model, paying due consideration to the average size of direct writing companies in Japan; 4) I determined the rule for appropriating and disposing the RCL, and assumed a plural pattern for RCL. I assumed 3 patterns for the RCL as folJows: • A pattern which has no RCL Pattern 0 • A pattern with which the appropriation rate of RCL is 2% Pattern 2 • A pattern with which the appropriation rate of RCL is ~
~~rn4