Description: This is a study on the Nesbitt formula and the variants to this formula.

Description: It has been twenty years since DeWit 1982 first applied fuzzy logic FL to insurance. That article sought to quantify the fuzziness in underwriting. Since then, the universe of discourse has expanded considerably and now the FL methodologies include used fuzzy set theory, fuzzy numbers and fuzzy arithmetic, fuzzy inference systems, fuzzy clustering algorithms, fuzzy linear programming, fuzzy regression, and hybrids involving other soft computing technologies. This article presents an overview of these studies.

Description: This is a presentation from 39th Actuarial Research Conference, 8/5-7/2004, University of Iowa in Iowa City, Iowa. This paper discusses the reserving of claims when there are negative values in the runoff triangle. It uses the Bayesian analysis method using the three-parameter log-normal distribution.

Description: This is a presentation from 43rd Actuarial Research Conference ARC, Regina, August 14–16, 2008. This talk will present the moment generating function of the discounted compound Poisson aggregate sums when the deflated claims are PH distributed and moment generating function of the discounted compound renewal sums.

Description: This research was funded by the Natural Sciences and Engineering Research Council of Canada [NSERC] Discovery Grant 36860–06. Loss reserving is one of the most challenging tasks facing actuaries. Numerous approaches have been developed to give reasonable estimates. Generalized linear models [GLMs] are becoming quickly popular statistical analysis methods to estimate loss reserves. However, most of these models are aggregate reserving methods based on loss development triangles, without using information with regard to the actual claims processes. This paper establishes a more sophisticated structural reserving method incorporating more detailed information, such as the premium exposure emergence pattern, the loss emergence pattern and the loss development pattern, within the framework of GLMs.

Description: In this paper, chapter III of the 1987 Valuation Actuary Handbook, the authors discuss building a liability model to evaluate the C-3 risk. The article discusses the data and assumptions needed, and the importance of sensitivity testing given that the model results are very sensitive to the assumptions used.

Description: ETFs have seen explosive growth in the past decade. Due to its flexibility and embedded risk management features, insurance companies and pension funds, are showing increasing interest in this asset class. This session covers an introduction to ETFs and the risk/rewards for insurance companies and pension funds as an additional asset class.

Description: This is a proof on Lidstone's theorem. It contains formulas for calculating policy dividends.

Description: This is a simplified approach to calculating the variance of the whole life random variable in certain, very common circumstances.

Description: This is a summary of the presentation given during the ARC Conference. Its purpose was to give a brief introduction to subexponential behavior and to show that the family of subexponential distributions provides ideal characteristics to model insurance risks. Although the literature related to this topic accumulated quickly during the last years, a textbook explaining the applications of extreme value theory with intuition as well as insight was still to be written. Embrechts et al, {I 997} satisfies this need and most of the results presented here can be found in this new classic in the actuarial literature.