Loss Reserve Estimates: A Statistical Approach for Determining "Reasonableness"

By Mark R. Shapland

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While accounting principles and actuarial standards of practice are all well designed, they provide only broad guidance to the actuary on what is “reasonable.” This broad guidance is based on the principle that “reasonable” assumptions and methods lead to “reasonable” estimates. Unfortunately, this broad guidance can leave the low end of a range of “reasonable” reserves open to an interpretation that could lead to unintended consequences in practice. This paper reviews some current actuarial practices and examines how they relate to the question of what is “reasonable” from a statistical perspective.Moreover, it reviews and further develops some statistical concepts and principles that actuaries can add to their repertoire when developing ranges and distributions of liability estimates and then evaluating the “reasonableness” of management’s best estimate within those ranges and distributions. KEYWORDS: Reasonable reserve, reserve variability, reserve range, reserve distribution, best estimate, risk margin, unpaid claim liability, deterministic methods, stochastic models

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Shapland, Mark R., "Loss Reserve Estimates: A Statistical Approach for Determining "Reasonableness"," Variance 1:1, 2007, pp. 120-148.

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Variance (ISSN 1940-6452) is a peer-reviewed journal published by the Casualty Actuarial Society to disseminate work of interest to casualty actuaries worldwide. The focus of Variance is original practical and theoretical research in casualty actuarial science. Significant survey or similar articles are also considered for publication. Membership in the Casualty Actuarial Society is not a prerequisite for submitting papers to the journal and submissions by non-CAS members is encouraged.