Modeling Dependence Between Loss Triangles
17 Pages Posted: 25 Mar 2009 Last revised: 24 Mar 2011
Date Written: April 17, 2009
A critical problem in property and casualty insurance is forecasting incurred but as yet unpaid losses. Forecasts and risk margins are often based on individual loss triangles with each triangle corresponding to a different line of business. However lines of business are often related and an overall risk margins must reflect dependence between triangles. This article develops, implements and applies a model for loss triangle dependence. The model relates payments in different triangles in the same calendar year. Dependence is modeled with a Gaussian copula correlation matrix. Correlations are moderated by quantities called communalities which measure the relative impact of cross dependence in each triangle. Correlations can be structured in terms of factor models. Methods reduce to relatively simple calculations in the case of marginal normal distribution. Procedures are applied to US loss triangle data and the impact of loss triangle dependence on risk margins is considered.
Keywords: Copulas, Gaussian Copula, Specificity, Communality, Loss triangles, Forecasting, Diversification benefits
JEL Classification: C51, C53, D81, G22
Suggested Citation: Suggested Citation