Excess Based Allocation of Risk Capital
AbstractIn this paper we propose a new rule to allocate risk capital to portfolios or divisions within a firm. Specifically, we determine the capital allocation that minimizes the excesses of sets of portfolios in lexicographical sense. The excess of a set of portfolios is defined as the expected loss of that set of portfolios in excess of the amount of risk capital allocated to them. The underlying idea is that large excesses are undesirable, and therefore the goal is to determine the allocation for which the largest excess is as small as possible. We show that this allocation rule yields a unique allocation, and that it satisfies some desirable properties. We also show that the allocation can be determined by solving a series of linear programming problems.
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Bibliographic InfoPaper provided by Tilburg University, Center for Economic Research in its series Discussion Paper with number 2010-123.
Date of creation: 2010
Date of revision:
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Web page: http://center.uvt.nl
risk capital; capital allocation; excesses; lexicographic minimum;
Other versions of this item:
- G10 - Financial Economics - - General Financial Markets - - - General (includes Measurement and Data)
- C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
- C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games
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- Dhaene, J. & Henrard, L. & Landsman, Z. & Vandendorpe, A. & Vanduffel, S., 2008. "Some results on the CTE-based capital allocation rule," Insurance: Mathematics and Economics, Elsevier, vol. 42(2), pages 855-863, April.
- Fischer, T., 2003. "Risk capital allocation by coherent risk measures based on one-sided moments," Insurance: Mathematics and Economics, Elsevier, vol. 32(1), pages 135-146, February.
- Jennifer L. Wang & H.C. Huang & Sharon S. Yang & Jeffrey T. Tsai, 2010. "An Optimal Product Mix for Hedging Longevity Risk in Life Insurance Companies: The Immunization Theory Approach," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 77(2), pages 473-497.
- De Waegenaere, A.M.B. & Melenberg, B. & Stevens, R., 2010.
Open Access publications from Tilburg University
urn:nbn:nl:ui:12-4578387, Tilburg University.
- Furman, Edward & Zitikis, Ricardas, 2008. "Weighted risk capital allocations," Insurance: Mathematics and Economics, Elsevier, vol. 43(2), pages 263-269, October.
- Michael Sherris, 2006. "Solvency, Capital Allocation, and Fair Rate of Return in Insurance," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 73(1), pages 71-96.
- Tsanakas, Andreas, 2004. "Dynamic capital allocation with distortion risk measures," Insurance: Mathematics and Economics, Elsevier, vol. 35(2), pages 223-243, October.
- Carlo Acerbi & Dirk Tasche, 2001.
"On the coherence of Expected Shortfall,"
cond-mat/0104295, arXiv.org, revised May 2002.
- Maschler, M. & Potters, J.A.M. & Tijs, S.H., 1992. "The general nucleolus and the reduced game property," Open Access publications from Tilburg University urn:nbn:nl:ui:12-154217, Tilburg University.
- Laeven, Roger J. A. & Goovaerts, Marc J., 2004. "An optimization approach to the dynamic allocation of economic capital," Insurance: Mathematics and Economics, Elsevier, vol. 35(2), pages 299-319, October.
- Tsanakas, Andreas, 2009. "To split or not to split: Capital allocation with convex risk measures," Insurance: Mathematics and Economics, Elsevier, vol. 44(2), pages 268-277, April.
- Jan Dhaene & Andreas Tsanakas & Emiliano A. Valdez & Steven Vanduffel, 2012.
"Optimal Capital Allocation Principles,"
Journal of Risk & Insurance,
The American Risk and Insurance Association, vol. 79(1), pages 1-28, 03.
- Tsanakas, Andreas & Barnett, Christopher, 2003. "Risk capital allocation and cooperative pricing of insurance liabilities," Insurance: Mathematics and Economics, Elsevier, vol. 33(2), pages 239-254, October.
- Kaas, Rob & Laeven, Roger J.A. & Nelsen, Roger B., 2009. "Worst VaR scenarios with given marginals and measures of association," Insurance: Mathematics and Economics, Elsevier, vol. 44(2), pages 146-158, April.
- Carter, Lawrence R. & Lee, Ronald D., 1992. "Modeling and forecasting US sex differentials in mortality," International Journal of Forecasting, Elsevier, vol. 8(3), pages 393-411, November.
- Müller, Alfred & Scarsini, Marco, 2000. "Some Remarks on the Supermodular Order," Journal of Multivariate Analysis, Elsevier, vol. 73(1), pages 107-119, April.
- Kim, Joseph H.T. & Hardy, Mary R., 2009. "A capital allocation based on a solvency exchange option," Insurance: Mathematics and Economics, Elsevier, vol. 44(3), pages 357-366, June.
- Koster, M.A.L., 1999. "Cost Sharing in Production Situations and Network Exploitation," Open Access publications from Tilburg University urn:nbn:nl:ui:12-80718, Tilburg University.
- Joe, Harry, 1990. "Multivariate concordance," Journal of Multivariate Analysis, Elsevier, vol. 35(1), pages 12-30, October.
- Pitacco, Ermanno & Denuit, Michel & Haberman, Steven & Olivieri, Annamaria, 2009. "Modelling Longevity Dynamics for Pensions and Annuity Business," OUP Catalogue, Oxford University Press, number 9780199547272, October.
- Maschler, M & Potters, J A M & Tijs, S H, 1992. "The General Nucleolus and the Reduced Game Property," International Journal of Game Theory, Springer, vol. 21(1), pages 85-106.
- Tsai, Jeffrey T. & Wang, Jennifer L. & Tzeng, Larry Y., 2010. "On the optimal product mix in life insurance companies using conditional value at risk," Insurance: Mathematics and Economics, Elsevier, vol. 46(1), pages 235-241, February.
- Peter C. Fishburn, 1974. "Exceptional Paper--Lexicographic Orders, Utilities and Decision Rules: A Survey," Management Science, INFORMS, vol. 20(11), pages 1442-1471, July.
- Philippe Artzner & Freddy Delbaen & Jean-Marc Eber & David Heath, 1999. "Coherent Measures of Risk," Mathematical Finance, Wiley Blackwell, vol. 9(3), pages 203-228.
- Boonen, T.J. & De Waegenaere, A.M.B. & Norde, H.W., 2012. "A Generalization of the Aumann-Shapley Value for Risk Capital Allocation Problems," Discussion Paper 2012-091, Tilburg University, Center for Economic Research.
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