Description: This paper develops credibility using a longitudinal data framework. In a longitudinal data framework, one might encounter data from a cross-section of risk classes towns with a history of insurance claims available for each risk class. For the marginal claims distributions, we use generalized linear models, an extension of linear regression that also encompasses Weibull and Gamma regressions. Copulas are used to model the dependencies over time specifically, this paper is the first to propose using a t-copula in the context of generalized linear models. The t-copula is the copula associated with the multivariate t-distribution like univariate t-distributions, it seems especially suitable for empirical work. Moreover, we show that the t-copula gives rise to easily computable predictive distributions that we use to generate credibility predictors. Like Bayesian methods, our copula credibility prediction methods allow us to provide an entire distribution of predicted claims, not just a point prediction.

Description: The purpose of this paper is to provide a method for calculating special contingency reserves for investment losses. The method is derived by first building a stochastic investment model and then utilizing its probabilistic structure. From Transactions of Society of Actuaries 1980, Vol. 32.

Description: From a session at the Spring meeting of the Society of Actuaries held in San Antonio, Texas, June 14-15, 2004 The panelists discuss the benefits of hedging variable annuity guarantees, the challenges they face and how they keep score.

Description: We consider Libor market model and calibration process. We estimate some interest rate derivatives such as Caps and Swaptions. We use Monte Carlo methods with appropriate dynamics under spot measure and forward measure. Imposing martingale discretization property, the same quantities are estimated again to see a contrast or discrepancy in light of confidence interval. Based on algorithms discussed in the paper, “Arbitrage-free discretizations of lognormal forward Libor and swap rate models” by Glasserman, P and Zhao, X 2000, the algorithms are implemented in excel VBA. Starting with current market data such as FRAs and Bond Prices, we describe steps involved to estimate the price of interest rate derivatives such as Caps and Swaptions, which would be beneficial to the practitioners in the industry.

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: This paper is Part 1 of a two-part submission. Part 2, “An Alternative Approach to Capital Allocation,” discusses using risk-replicating techniques that directly calculate the cost of capital. Such techniques can be used as a substitute for capital allocation. This paper expands upon current capital analysis by introducing a practical approach that considers the objectives of all stakeholders of an insurance company in setting appropriate capital targets.

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.

Description: We consider a class of compound renewal risk process with claim waiting times have a discrete Km distribution. The classical compound binomial risk model is a special case when m = 1. Both recursive and explicit formulas are derived for the expected discounted penalty function due at ruin, for the surplus before ruin and the deficit at ruin. Many ruin related quantities can be analyzed through the penalty function, e.g., ruin probability, the p.g.f. of the time of ruin, joint and marginal distributions of the surplus before ruin and the deficit at ruin, claim causing ruin, as well as their moments. Detailed discussions are given in two special cases: claim sizes are rationally distributed, or the claim sizes distribution have a finite support.

Description: This is the abstract of the paper 'A Stochastic Definition of Future Shares'. The traditional definition of actuarial future values and stochastic definition of Ramsay are discussed. A modification of Ramsay's definition is proposed and an application to life insurance reserves is presented.