Modeling Dependence Between Loss Triangles

17 Pages Posted: 25 Mar 2009 Last revised: 24 Mar 2011

See all articles by Piet De Jong

Piet De Jong

Macquarie University - Department of Applied Finance and Actuarial Studies; Financial Research Network (FIRN); Macquarie University, Macquarie Business School

Date Written: April 17, 2009

Abstract

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

De Jong, Piet, Modeling Dependence Between Loss Triangles (April 17, 2009). Available at SSRN: https://ssrn.com/abstract=1367942 or http://dx.doi.org/10.2139/ssrn.1367942

Piet De Jong (Contact Author)

Macquarie University - Department of Applied Finance and Actuarial Studies ( email )

Sydney, New South Wales
Australia

Financial Research Network (FIRN)

C/- University of Queensland Business School
St Lucia, 4071 Brisbane
Queensland
Australia

HOME PAGE: http://www.firn.org.au

Macquarie University, Macquarie Business School ( email )

New South Wales 2109
Australia

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