Egalitarian equivalent capital allocation. (English) Zbl 1414.91206

Kamiya, Shinichi; Zanjani, George

N. Am. Actuar. J. 21, No. 3, 382-396 (2017).

Summary: We apply Moulin’s notion of egalitarian equivalent cost sharing of a public good to the problem of insurance capitalization and capital allocation where the liability portfolio is fixed. We show that this approach yields overall capitalization and cost allocations that are Pareto efficient, individually rational, and, unlike other mechanisms, stable in the sense of adhering to cost monotonicity.

MSC:

91B30	Risk theory, insurance (MSC2010)
91B18	Public goods
91B32	Resource and cost allocation (including fair division, apportionment, etc.)

Keywords:

egalitarian equivalent cost sharing; public good; insurance capitalization; capital allocation

References:

[1]	Bauer, D.; Zanjani, G.; Dionne, G., Handbook of Insurance, Capital Allocation and Its Discontents, 863-880, (2013), New York: Springer, New York
[2]	Bauer, D.; Zanjani, G., The Marginal Cost of Risk in a Multi-Period Model, Casualty Actuarial Society Research Report, (2013)
[3]	Bauer, D.; Zanjani, G., The Marginal Cost of Risk, Risk Measures, and Capital Allocation, Management Science, 62, 1431-1457, (2016)
[4]	Denault, M., Coherent Allocation of Risk Capital, Journal of Risk, 4, 7-21, (2001)
[5]	Dhaene, J.; Tsanakas, A.; Valdez, E. A.; Vanduffel, S., Optimal Capital Allocation Principles, Journal of Risk and Insurance, 79, 1-28, (2012)
[6]	Dhaene, J. L. M.; Goovaerts, M. J.; Kaas, R., Economic Capital Allocation Derived from Risk Measures, North American Actuarial Journal, 7, 44-59, (2003) · Zbl 1084.91515
[7]	Foley, D., Lindahl’s Solution and the Core of an Economy with Public Goods, Econometrica, 38, 66-72, (1970) · Zbl 0196.23406
[8]	Kalkbrener, M., An Axiomatic Approach to Capital Allocation, Mathematical Finance, 15, 425-37, (2005) · Zbl 1102.91049
[9]	Kaneko, M., The Ratio Equilibrium and a Voting Game in a Public Good Economy, Journal of Economic Theory, 16, 123-136, (1977) · Zbl 0399.90019
[10]	Kou, S.; Peng, X.; Heyde, C. C., External Risk Measures and Basel Accords, Mathematics of Operations Research, 38, 393-417, (2013) · Zbl 1297.91089
[11]	Laeven, R. J. A.; Goovaerts, M. J., An Optimization Approach to the Dynamic Allocation of Economic Capital, Insurance: Mathematics and Economics, 35, 299-319, (2004) · Zbl 1079.91037
[12]	Lindahl, Erik.; Musgrave, Richard A.; Peacock, Alan T., Classics in the Theory of Public Finance, Just Taxation-A Positive Solution. Reprinted in part, 168-176, (1958), London: Macmillan, London
[13]	Mas-Colell, A.; Silvestre, J., Cost Share Equilibria: A Lindahlian Approach, Journal of Economic Theory, 47, 239-256, (1989) · Zbl 0672.90020
[14]	Merton, R. C.; Perold, A. F., Theory of Risk Capital in Financial Firms, Journal of Applied Corporate Finance, 6, 16-32, (1993)
[15]	Meyers, G. G., The Economics of Capital Allocation, 391-418, (2003)
[16]	Moulin, H., Egalitarian-Equivalent Cost Sharing of a Public Good, Econometrica, 55, 963-976, (1987) · Zbl 0619.90004
[17]	Myers, S. C.; Read, J. A., Capital Allocation for Insurance Companies, Journal of Risk and Insurance, 68, 545-580, (2001)
[18]	Pazner, E.; Schmeidler, D., Egalitarian Equivalent Allocations: A New Concept of Economic Equity, Quarterly Journal of Economics, 92, 671-686, (1978)
[19]	Powers, M. R., Using Aumann-Shapley Values to Allocate Insurance Risk: The Case of Inhomogeneous Losses, North American Actuarial Journal, 11, 113-127, (2007)
[20]	Stoughton, N. M.; Zechner, J., Optimal Capital Allocation Using RAROC and EVA, Journal of Financial Intermediation, 16, 312-342, (2007)
[21]	Tasche, D.; Dev, A., Economic Capital: A Practitioner Guide, Allocating Portfolio Economic Capital to Sub-portfolios, 275-302, (2004), Risk Books
[22]	Tsanakas, A.; Barnett, C., Risk Capital Allocation and Cooperative Pricing of Insurance Liabilities, Insurance: Mathematics and Economics, 33, 239-254, (2003) · Zbl 1103.91317
[23]	Zanjani, G., Pricing and Capital Allocation in Catastrophe Insurance, Journal of Financial Economics, 65, 283-305, (2002)
[24]	Zanjani, G., An Economic Approach to Capital Allocation, Journal of Risk and Insurance, 77, 523-549, (2010)