AGGREGATION OF CORRELATED RISK PORTFOLIOS: MODELS AND ALGORITHMS

Shaun Shuxun Wang · Ken Seng Tan

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Probability and Risk Models Financial Risk and Volatility Modeling Risk and Portfolio Optimization

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.

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References

1979The impact of heterogeneity in individual frailty on the dynamics of mortality 1982A distribution-free approach to inducing rank correlation among input variables 1998Understanding Relationships Using Copulas 1999Loss Models: From Data to Decisions 1986The Joy of Copulas: Bivariate Distributions with Uniform Marginals 1981Recursive Evaluation of a Family of Compound Distributions 1987The Poisson-Inverse Gaussian distribution as an alternative to the negative binomial 1999Loss Models: from Data to Decisions. By Stuart Klugman, Harry Panjer and Gordon Willmot [John Wiley & Sons, New York, 1998]

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2008On the compound Poisson risk model with dependence based on a generalized Farlie–Gumbel–Morgenstern copula 1998Modeling and Comparing Dependencies in Multivariate Risk Portfolios 2003Risk Measurement, Risk Management, and Capital Adequacy in Financial Conglomerates 2004A General Approach to Integrated Risk Management with Skewed, Fat-Tailed Risk 2013TAILS OF COPULAS

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