New Actuarial Science Findings from Harvard University Described (Comparison Of Approximations For Compound Poisson Processes)

By a News Reporter-Staff News Editor at Insurance Weekly News -- Fresh data on Actuarial Science are presented in a new report. According to news reporting out of Cambridge, Massachusetts, by VerticalNews editors, research stated, "In this paper, we compare the error in several approximation methods for the cumulative aggregate claim distribution customarily used in the collective model of insurance theory. In this model, it is usually supposed that a portfolio is at risk for a time period of length t. The occurrences of the claims are governed by a Poisson process of intensity mu so that the number of claims in [0, t] is a Poisson random variable with parameter lambda = mu t. Each single claim is an independent replication of the random variable X, representing the claim severity."

Our news journalists obtained a quote from the research from Harvard University, "The aggregate claim or total claim amount process in [0, t] is represented by the random sum of N independent replications of X, whose cumulative distribution function (cdf) is the object of study. Due to its computational complexity, several approximation methods for this cdf have been proposed. In this paper, we consider 15 approximations put forward in the literature that only use information on the lower order moments of the involved distributions. For each approximation, we consider the difference between the true distribution and the approximating one and we propose to use expansions of this difference related to Edgeworth series to measure their accuracy as lambda = mu t diverges to infinity. Using these expansions, several statements concerning the quality of approximations for the distribution of the aggregate claim process can find theoretical support. Other statements can be disproved on the same grounds."

According to the news editors, the research concluded: "Finally, we investigate numerically the accuracy of the proposed formulas."

For more information on this research see: Comparison Of Approximations For Compound Poisson Processes. Astin Bulletin, 2015;45(3):601-637. Astin Bulletin can be contacted at: Cambridge Univ Press, Edinburgh Bldg, Shaftesbury Rd, CB2 8RU Cambridge, England.

Our news journalists report that additional information may be obtained by contacting R. Seri, IQSS Harvard Univ, Cambridge, MA 02138, United States.

Keywords for this news article include: Cambridge, Massachusetts, United States, Actuarial Science, North and Central America

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