Aggregation of Correlated Risk Portfolios: Models & Algorithms

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Aggregation of Correlated Risk Portfolios: Models & Algorithms

by Shaun S. Wang for the CAS Committee on Theory of Risk

November 1998

Abstract: Aggregate loss distributions are probability distributions of the total dollar amount of loss under one or a block of insurance policies. They combine the separate effects of the underlying frequency and severity distributions. In the actuarial literature, a number of methods have been developed for modeling and computing the aggregate loss distributions, see Heckman & Meyers (1983), Panjer (1981) and Robertson (1992). The main issue underlying this research project is how to combine aggregate loss distributions for separate but correlated classes of business.

Assume a book of business is the union of disjoint classes of business each of which has an aggregate distribution. These distributions may be given in many different ways. Among other ways, they may be specified parametrically, e.g. lognormal or transformed beta with given parameters; they may be given by specifying separate frequency and severity distributions; e.g. negative binomial frequency and pareto severity with given parameters. The classes of business are NOT independent. For this project, assume that we are given a correlation matrix (or some other easily obtainable measure of dependency) and that the correlation coefficients vary among different pairs of classes. The problem is how to calculate the aggregate loss distribution for the whole book.

Published in: Proceedings of the Casualty Actuarial Society, Vol. 85, No. 163, (November 1998), pp. 848-937.

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