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Suitability of Capital Allocations for Performance Measurement

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  • Eduard Kromer
  • Ludger Overbeck

Abstract

Capital allocation principles are used in various contexts in which a risk capital or a cost of an aggregate position has to be allocated among its constituent parts. We study capital allocation principles in a performance measurement framework. We introduce the notation of suitability of allocations for performance measurement and show under different assumptions on the involved reward and risk measures that there exist suitable allocation methods. The existence of certain suitable allocation principles generally is given under rather strict assumptions on the underlying risk measure. Therefore we show, with a reformulated definition of suitability and in a slightly modified setting, that there is a known suitable allocation principle that does not require any properties of the underlying risk measure. Additionally we extend a previous characterization result from the literature from a mean-risk to a reward-risk setting. Formulations of this theory are also possible in a game theoretic setting.

Suggested Citation

  • Eduard Kromer & Ludger Overbeck, 2013. "Suitability of Capital Allocations for Performance Measurement," Papers 1301.5497, arXiv.org, revised Jul 2014.
    • Handle: RePEc:arx:papers:1301.5497
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    Cited by:

    1. Regele, Fabian & Gründl, Helmut, 2021. "Asset concentration risk and insurance solvency regulation," ICIR Working Paper Series 40/21, Goethe University Frankfurt, International Center for Insurance Regulation (ICIR).
    2. E. Kromer & L. Overbeck & K. Zilch, 2016. "Systemic risk measures on general measurable spaces," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 84(2), pages 323-357, October.

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