Severity Curve Fitting for Long­Tailed Lines: An Application of Stochastic Processes and Bayesian Models

By Gregory F. McNulty

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Abstract

I present evidence for a model in which parameters fit to the severity distribution at each report age follow a smooth curve with random error. More formally, this is a stochastic process, and it allows us to estimate parameters of the ultimate severity distribution. I detail a Bayesian hierarchical model that takes a modestly sized dataset of triangulated individual claim data and returns posterior distributions for the parameters of the ultimate severity distribution, trend and loss to an excess layer. Currently available methods are also discussed. Full code and data are provided in the appendices.

Keywords: Bayesian hierarchical models, stochastic processes, severity distributions, reinsurance pricing

Citation

McNulty, Gregory F., "Severity Curve Fitting for Long­Tailed Lines: An Application of Stochastic Processes and Bayesian Models," Variance 11:1, 2018, pp. 118-132.

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Mission Statement

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.