Hostname: page-component-cd9895bd7-8ctnn Total loading time: 0 Render date: 2024-12-26T22:57:54.672Z Has data issue: false hasContentIssue false
  • English
  • Français

Determining and Allocating Diversification Benefits for a Portfolio of Risks

Published online by Cambridge University Press:  09 August 2013

Weihao Choo  and
Piet de Jong
Weihao Choo
Affiliation:
Department of Actuarial Studies, Macquarie UniversityNSW 2109, Australia
Get access Rights & Permissions [Opens in a new window]

Abstract

A critical problem in financial and insurance risk analysis is the calculation of risk margins. When there are a number of risks, the total risk margin is often reduced to reflect diversification. How large should the “diversification benefit” be? And how should the benefit be allocated to the individual risks? We propose a simple statistical solution. While providing a theoretical analysis, the final expressions are readily implemented in practice.

Keywords

DiversificationAllocated risk marginsStand-alone risk marginsCapital allocationEuler allocationPercentile risk aversion
Type
Research Article
Information
ASTIN Bulletin: The Journal of the IAA , Volume 40 , Issue 1 , May 2010 , pp. 257 - 269
Copyright
Copyright © International Actuarial Association 2010

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Acerbi, C. (2002) Spectral measures of risk: a coherent representation of subjective risk aversion. Journal of Banking and Finance 26(7), 1505–1518.CrossRefGoogle Scholar
Billera, L. and Heath, D. (1982) Allocation of shared costs: A set of axioms yielding a unique procedure. Mathematics of Operations Research, 32–39.Google Scholar
Choo, W. and De Jong, P. (2009) Loss Reserving Using Loss Aversion Functions. SSRN eLibrary – forthcoming Insurance, Mathematics & Economics.Google Scholar
Dhaene, J., Tsanakas, A., Valdez, E.A. and Vanduffel, S. (2009) Optimal Capital Allocation Principles. SSRN eLibrary.Google Scholar
Furman, E. and Landsman, Z. (2008) Economic capital allocations for non-negative portfolios of dependent risks. ASTIN Bulletin 38(2), 601–619.Google Scholar
Furman, E. and Zitikis, R. (2008a) Weighted premium calculation principles. Insurance Mathematics and Economics 42(1), 459–465.Google Scholar
Furman, E. and Zitikis, R. (2008b) Weighted risk capital allocations. Insurance Mathematics and Economics 43(2), 263–269.Google Scholar
Furman, E. and Zitikis, R. (2009) General Stein-type Covariance Decompositions with Applications to Insurance and Finance. In Blose, L.E. (ed.), Proceedings of the 58th Annual Meeting of the Midwest Finance Association, Volume 6.Google Scholar
Heilmann, W (1989) Decision theoretic foundations of credibility theory. Insurance Mathematics & Economics 8(1), 77–95.Google Scholar
Kalkbrener, M. (2005) An axiomatic approach to capital allocation. Mathematical Finance 15(3), 425–437.Google Scholar
Kreps, R. (2005) Riskiness Leverage Models. Proceedings of the Casualty Actuarial Society (PCAS) 92, 31–60.Google Scholar
Lighthill, M. (1958) Introduction to Fourier analysis and generalised functions. Cambridge: Cambridge university Press.CrossRefGoogle Scholar
Luenberger, D. (1998) Investment Science. Oxford University Press, USA.Google Scholar
Mcneil, A., Frey, R. and Embrechts, P. (2005) Quantitative risk management. Princeton University Press.Google Scholar
Mirman, L. and Tauman, Y. (1982) Demand compatible equitable cost sharing prices. Mathematics of Operations Research, 40–56.Google Scholar
Overbeck, L. (2004) Spectral capital allocation. In Dev, A. (ed.), Economic capital: a practitioner guide, pp. 303–313. London: Risk Books.Google Scholar
Quiggin, J. (1982) A theory of anticipated utility. Journal of Economic Behavior and Organization 3(A), 323–343.Google Scholar
Ruhm, D., Mango, D. and Total, R. (2003) A Risk Charge Calculation Based on Conditional Probability. Risk 200 (60), 1–268.Google Scholar
Tasche, D. (2001) Conditional expectation as quantile derivative. Arxivpreprint math.PR/0104190.Google Scholar
Tasche, D. (2004) Allocating portfolio economic capital to sub-portfolios. Econonomic Capital; A Practitioner Guide, Dev. A.(Ed.), Risk Books, 275–302.Google Scholar
Tsanakas, A. and Barnett, C. (2003) Risk capital allocation and cooperative pricing of insurance liabilities. Insurance Mathematics and Economics 33(2), 239–254.Google Scholar
Wang, S. (1996) Premium Calculation by Transforming the Premium Layer Density. ASTIN Bulletin 26(1), 71–92.Google Scholar
Yaari, M. (1987). The dual theory of choice under risk. Econometrica 55(1), 95–115.Google Scholar
Zaks, Y., Frostig, E. and Levikson, B. (2006) Optimal pricing of a heterogeneous portfolio for a given risk level. ASTIN Bulletin 36(1), 161.Google Scholar