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Comparison between Financial Theory and Cooperative Game Theory in Risk Capital Allocation

Author

Listed:
  • Seog S. Hun

    (Seoul National University)

  • Shin Sungwhee

    (University of Seoul)

Abstract

We compare two prominent approaches to capital allocation in insurance firms. The financial theory approach includes Merton and Perold (1993) and Myers and Read (2001). The cooperative game theory approach utilizes concepts such as the Shapley value and the Aumann-Shapley value. We argue that, when an entire division is added or when the effect of a decision is discrete, the Shapley value approach provides an improvement over the Merton and Perold approach in that it properly accounts for the order in which divisions are added, and resoles the unallocated capital problem. When the effect of a decision is continuous, we show that the Auman-Shapley value approach not only provides game theoretic support for, but also conceptually extends, the Myers and Read approach.

Suggested Citation

  • Seog S. Hun & Shin Sungwhee, 2009. "Comparison between Financial Theory and Cooperative Game Theory in Risk Capital Allocation," Asia-Pacific Journal of Risk and Insurance, De Gruyter, vol. 4(1), pages 1-18, November.
    • Handle: RePEc:bpj:apjrin:v:4:y:2009:i:1:n:1
    DOI: 10.2202/2153-3792.1047
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    References listed on IDEAS

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    1. Stephen Mildenhall, 2004. "A Note on the Myers and Read Capital Allocation Formula," North American Actuarial Journal, Taylor & Francis Journals, vol. 8(2), pages 32-44.
    2. 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.
    3. Michael Powers, 2007. "Using Aumann-Shapley Values to Allocate Insurance Risk," North American Actuarial Journal, Taylor & Francis Journals, vol. 11(3), pages 113-127.
    4. Gary Venter, 2004. "Capital Allocation Survey with Commentary," North American Actuarial Journal, Taylor & Francis Journals, vol. 8(2), pages 96-107.
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