AGGREGATION OF CORRELATED RISK PORTFOLIOS: MODELS AND ALGORITHMS

Abstract

This paper presents a set of tools for modeling and combining correlated risks. Various correlation structures are generated using copula, common mixture, component, and distortion models. These correlation structures are specified in terms of (i) the joint cumulative distribution function or (ii) the joint characteristic function and lend themselves to efficient methods of aggregation by using Monte Carlo simulation or fast Fourier transform. ACKNOWLEDGEMENT The author wishes to thank the CAS Committee on Theory of Risk for initiating and supporting this research project. A special thanks goes to Phil Heckman and Glenn Meyers for providing numerous stimulating comments while overseeing the progress of this project. Phil Heckman, Stephen Mildenhall, Don Mango, Louise Francis, and the CAS Editorial Committee, in their thorough review of this paper, have provided many valuable comments which led to significant improvement of an earlier draft report. The author also thanks Ole Hesselager, Julia Wirch, and Ken Seng Tan for comments.