Dhaene, Jan and Tsanakas, Andreas and Emiliano, Valdez and Steven, Vanduffel (2009): Optimal capital allocation principles.

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Abstract
This paper develops a unifying framework for allocating the aggregate capital of a financial firm to its business units. The approach relies on an optimisation argument, requiring that the weighted sum of measures for the deviations of the business unit’s losses from their respective allocated capitals be minimised. This enables the association of alternative allocation rules to specific decision criteria and thus provides the risk manager with flexibility to meet specific target objectives. The underlying general framework reproduces many capital allocation methods that have appeared in the literature and allows for several possible extensions. An application to an insurance market with policyholder protection is additionally provided as an illustration.
Item Type:  MPRA Paper 

Original Title:  Optimal capital allocation principles 
Language:  English 
Keywords:  Capital allocation; risk measure; comonotonicity; Euler allocation; default option; Lloyd’s of London 
Subjects:  G  Financial Economics > G0  General > G00  General G  Financial Economics > G2  Financial Institutions and Services > G20  General 
Item ID:  13574 
Depositing User:  Emiliano Valdez 
Date Deposited:  22. Feb 2009 02:00 
Last Modified:  13. Feb 2013 15:45 
References:  C. Acerbi. Spectral measures of risk: a coherent representation of subjective risk aversion. Journal of Banking and Finance, 26(7):1505–1518, 2002. C. Acerbi and D. Tasche. On the coherence of expected shortfall. Journal of Banking and Finance, 26(7):1487–1503, 2002. P. Artzner, F. Delbaen, J.M. Eber, and D. Heath. Coherent measures of risk. Mathematical Finance, 9(3):203–228, 1999. H. Buhlmann. Mathematical Methods in Risk Theory. SpringerVerlag, Berlin, 1970. J.D. Cummins. Allocation of capital in the insurance industry. Risk Management and Insurance Review, 3(1):7–27, 2000. M. Denault. Coherent allocation of risk capital. Journal of Risk, 4(1):1–34, 2001. J. Dhaene, M. Denuit, M.J. Goovaerts, R. Kaas, and D. Vyncke. The concept of comonotonicity in actuarial science and finance: theory. Insurance: Mathematics and Economics, 31:3–33, 2002. J. Dhaene, M.J. Goovaerts, and R. Kaas. Economic capital allocation derived from risk measures. North American Actuarial Journal, 7(2):44–59, 2003. J. Dhaene, S. Vanduffel, Q. Tang, M.J. Goovaerts, R. Kaas, and D. Vyncke. Risk measures and comonotonicity: a review. Stochastic Models, 22(4):573–606, 2006. J. Dhaene, L. Henrard, Z. Landsman, A. Vandendorpe, and S. Vanduffel. Some results on the CTE based capital allocation rule. Insurance: Mathematics and Economics, 42(2):855–863, 2008. J. Dhaene, M. Denuit, and S. Vanduffel. Correlation order, merging and diversification. Submitted, 2009. Available at http://www.econ.kuleuven.be/insurance/research.htm. H. Follmer and A. Schied. Convex measures of risk and trading constraints. Finance and Stochastics, 6(4):429–447, 2002. E. Furman and R. Zitikis. Weighted premium calculation principles. Insurance: Mathematics and Economics, 42(1):459–465, 2008a. E. Furman and R. Zitikis. Weighted risk capital allocations. Insurance: Mathematics and Economics, 43(2):263–269, 2008b. H.U. Gerber. On additive premium calculation principles. ASTIN Bulletin, 7(3):215–222, 1974. H.U. Gerber. The esscher premium principle: a criticism. comment. ASTIN Bulletin, 12(2): 139–140, 1981. M.J. Goovaerts, F. deVylder, and J. Haezendonck. Insurance Premiums: Theory and Applications. Amsterdam, North Holland, 1984. H. Grundl and H. Schmeiser. Capital allocation for insurance companies: what good is it? Journal of Risk and Insurance, 74(2):301–317, 2007. W.R. Heilmann. Decision theoretic foundations of credibility theory. Insurance: Mathematics and Economics, 8:77–95, 1989. M. Kalkbrener. An axiomatic approach to capital allocation. Mathematical Finance, 15(3):425–437, 2005. J. Kim and M. Hardy. A capital allocation based on a solvency exchange option. Insurance: Mathematics and Economics, 2008. In press. R.J.A. Laeven and M.J. Goovaerts. An optimization approach to the dynamic allocation of economic capital. Insurance: Mathematics and Economics, 35(2):299–319, 2004. Z. Landsman and E.A. Valdez. Tail conditional expectations for elliptical distributions. North American Actuarial Journal, 7(4):55–71, 2003. J. LeMaire. An application of game theory: cost allocation. ASTIN Bulletin, 14(1):61–81, 1984. Lloyd’s. Individual capital assessment (ICA) guidance. Working paper, 2008. Available at www.lloyds.com/Lloyds Market/Tools and reference/individual capital assessment guidance.htm. S.C. Myers and J.A. Read Jr. Capital allocation for insurance companies. Journal of Risk and Insurance, 68(4):545–580, 2001. L. Overbeck. Allocation of economic capital in loan portfolios. in J. Franke, W. Haerdle and G. Stahl (eds.), Measuring Risk in Complex Systems, Springer, 2000. H.H. Panjer. Measurement of risk, solvency requirements, and allocation of capital within financial conglomerates. Research Report 0114. Institute of Insurance and Pension Research, University of Waterloo, Canada, 2001. C.R. Rao. Statistics and Truth: Putting Chance to Work. World Scientific Publishing, River Edge, NJ, 1997. M. Sherris. Solvency, capital allocation and fair rate of return in insurance. Journal of Risk and Insurance, 73(1):71–96, 2006. D. Tasche. Allocating portfolio economic capital to subportfolios. In A. Dev (ed.), Economic Capital: A Practitioner’s Guide, Risk Books, pp. 275302, 2004. A. Tsanakas. Dynamic capital allocation with distortion risk measures. Insurance: Mathematics and Economics, 35(2):223–243, 2004. A. Tsanakas. Capital allocation with risk measures. Proceedings of the 5th Actuarial and Financial Mathematics Day, 9 February, Brussels, pp. 317, 2007. A. Tsanakas. To split or not to split: capital allocation with convex risk measures. Insurance: Mathematics and Economics, 2008. In press. E.A. Valdez and A. Chernih. Wang’s capital allocation formula for elliptically contoured distributions. Insurance: Mathematics and Economics, 33(3):517–532, 2003. G.G. Venter. Capital allocation survey with commentary. North American Actuarial Journal, 8(2):96–107, 2004. S.S. Wang. Premium calculation by transforming the premium layer density. ASTIN Bulletin, 26(1):71–92, 1996. S.S. Wang. Normalized exponential tilting: pricing and measuring multivariate risks. North American Actuarial Journal, 11(3):89–99, 2007. Y. Zaks, E. Frostig, and B. Levikson. Optimal pricing of a heterogeneous portfolio for a given risk level. ASTIN Bulletin, 36(1):161–185, 2006 
URI:  https://mpra.ub.unimuenchen.de/id/eprint/13574 