Description: This paper builds on a risk theory model described by Tellenbach [1977]. That model involves Laplace-Stieltjes transforms which pose severe computational difficulties. This paper describes a simple algorithm which appears to work in the special case where the time span considered is reasonably small. The latter condition is typically met if the model refers to cumulative claims. A thorough mathematical treatment of the subject is not even attempted. Rather, the emphasis is on the computational aspect of the problem.

Description: It is well-known that reinsurance can be an effective risk management technique for an insurer. An appropriate use of reinsurance reduces the adverse risk exposure of an insurer and improves the overall viability of the underlying business. The use of reinsurance, on the other hand, incurs additional cost to the insurer in the form of reinsurance premium. This implies that an insurer is faced with a classic tradeoff between risk spreading and risk retaining. The thrust of my research is to propose some reinsurance designs that are optimal from the perspective of an insurer. This presentation describes an empirical approach to optimal reinsurance designs. This new method has the advantage that it does not need to make any explicit assumptions on the distribution of the underling risk. More importantly, it provides a simple and yet practical way of obtaining solution on a wide range of optimal reinsurance models.

Description: The American Academy of Actuaries and the Society of Actuaries have joined resources to maintain this Economic Scenario Generators Excel Workbook tool for use in regulatory reserve and capital calculations. Please see the SOA website research pages for further information on this tool and how to use it.

Description: In problem 24, Chapter 5, of Kellison's 'Fundamentals of Numerical Analysis' it is indicated how a divided difference can be expressed as a ratio of two determinants. This study note shows that this method works well also in the case where some of the arguments of collocation coincide. The rule is: If an argument occurs k times, the derivatives of the corresponding row up to order k-1 should be used in numerator and denominator.

Description: This is a discussion of the paper, New Possibilities in Graduation by Kingsland Camp. From Transactions of Society of Actuaries 1955, Vol. 7, No. 19.

Description: This research paper presents two series formulas for the probability of eventual ruin derived by the operational calculus method. From the Actuarial Research Clearing House ARCH 1989 Vol. 1.

Description: The topic is graduation of raw mortality rates. The approach is to use operational bootstrapping, which produces results which could only be obtained by regular bootstrapping if an infinite number of random numbers were generated. From the Actuarial Research Clearing House 1994 Vol. 1 .

Description: Authored by a MIB Solutions team of Tom Rhodes, Stuart Klugman, Marianne Purushotham and Stacy Gill, the report summarizes the results of a study on the application and adoption of credibility theory within the life insurance and annuity industry. In addition to the report, numerical examples related to the application of credibility to company mortality and lapse data are provided in the four Excel files. This excel spreadsheet is a numerical example relating to the application of Credibility for lapses by policy for limited fluctuation. Please see the SOA website research section for the full report on Credibility Theory Practices.

Description: This short article provides a formulation for the Geometric Realization of Convolution of Uniform Distributions. From Actuarial Research Clearing House 1993, VOL. 2.

Description: Authored by a MIB Solutions team of Tom Rhodes, Stuart Klugman, Marianne Purushotham and Stacy Gill, the report summarizes the results of a study on the application and adoption of credibility theory within the life insurance and annuity industry. This excel spreadsheet is a numerical example relating to the application of Credibility for lapses. Please see the SOA website research section for the complete research report on Credibility Theory Practices.