Advances in Common Shock Modeling

By Z. Ming Li, Paul Gregory Ferrara

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Abstract

In this paper we rigorously investigate the common shock, or contagion, model, for correlating insurance losses. In addition, we develop additional theory which describes how the common shock model can be incorporated within a larger set of distributions. We also address the issue of calibrating contagion models to empirical data. To this end, we propose several procedures for calibrating contagion models using real-world industry data. Finally, we demonstrate the efficacy, and efficiency, of these calibration procedures by calibrating aggregate loss models, which incorporate contagion. Further, the case study illustrates the power of contagion modeling by demonstrating how the introduction of contagion can correct for the short-comings of traditional collective risk modeling.

Keywords: Aggregate Loss Models; Dynamic Risk Modeling

Citation

Li, Z. Ming, and Paul Gregory Ferrara, "Advances in Common Shock Modeling," Variance 9:1, 2015, pp. 20-35.

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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.