The center of a convex set and capital allocation

Bogdan Grechuk

European Journal of Operational Research, 2015, vol. 243, issue 2, 628-636

Abstract: A capital allocation scheme for a company that has a random total profit Y and uses a coherent risk measure ρ has been suggested. The scheme returns a unique real number Λρ*(X,Y), which determines the capital that should be allocated to company’s subsidiary with random profit X. The resulting capital allocation is linear and diversifying as defined by Kalkbrener (2005). The problem is reduced to selecting the “center” of a non-empty convex weakly compact subset of a Banach space, and the solution to the latter problem proposed by Lim (1981) has been used. Our scheme can also be applied to selecting the unique Pareto optimal allocation in a wide class of optimal risk sharing problems.

Keywords: Capital allocation; Risk contribution; Coherent risk measures; Risk sharing (search for similar items in EconPapers)
Date: 2015
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Citations: View citations in EconPapers (7)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:ejores:v:243:y:2015:i:2:p:628-636

DOI: 10.1016/j.ejor.2014.12.004

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