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Holistic principle for risk aggregation and capital allocation

Author

Listed:
  • Wing Fung Chong

    (University of Illinois at Urbana-Champaign
    University of Illinois at Urbana-Champaign)

  • Runhuan Feng

    (University of Illinois at Urbana-Champaign)

  • Longhao Jin

    (University of Illinois at Urbana-Champaign)

Abstract

Risk aggregation and capital allocation are of paramount importance in business, as they play critical roles in pricing, risk management, project financing, performance management, regulatory supervision, etc. The state-of-the-art practice often includes two steps: (i) determine standalone capital requirements for individual business lines and aggregate them at a corporate level; and (ii) allocate the total capital back to individual lines of business or at more granular levels. There are three pitfalls with such a practice, namely, lack of consistency, negligence of cost of capital, and disentanglement of allocated capitals from standalone capitals. In this paper, we introduce a holistic approach that aims to strike a balance of optimality by taking into account competing interests of various stakeholders and conflicting priorities in a corporate hierarchy. While unconventional in its objective, the new approach results in an allocation of diversification benefit, which conforms to the diversification strategy of many risk management frameworks including regulatory capital and economic capital. The holistic capital setting and allocation principle provides a remedy to aforementioned problems with the existing two-step industry practice.

Suggested Citation

  • Wing Fung Chong & Runhuan Feng & Longhao Jin, 2023. "Holistic principle for risk aggregation and capital allocation," Annals of Operations Research, Springer, vol. 330(1), pages 21-54, November.
  • Handle: RePEc:spr:annopr:v:330:y:2023:i:1:d:10.1007_s10479-021-03987-4
    DOI: 10.1007/s10479-021-03987-4
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    1. Buch, Arne & Dorfleitner, Gregor & Wimmer, Maximilian, 2011. "Risk capital allocation for RORAC optimization," Journal of Banking & Finance, Elsevier, vol. 35(11), pages 3001-3009, November.
    2. Di Lascio, F. Marta L. & Giammusso, Davide & Puccetti, Giovanni, 2018. "A clustering approach and a rule of thumb for risk aggregation," Journal of Banking & Finance, Elsevier, vol. 96(C), pages 236-248.
    3. Furman, Edward & Zitikis, Ricardas, 2008. "Weighted premium calculation principles," Insurance: Mathematics and Economics, Elsevier, vol. 42(1), pages 459-465, February.
    4. Perli, Roberto & Nayda, William I., 2004. "Economic and regulatory capital allocation for revolving retail exposures," Journal of Banking & Finance, Elsevier, vol. 28(4), pages 789-809, April.
    5. Zaks, Yaniv & Frostig, Esther & Levikson, Benny, 2006. "Optimal Pricing of a Heterogeneous Portfolio for a Given Risk Level," ASTIN Bulletin, Cambridge University Press, vol. 36(1), pages 161-185, May.
    6. Xiaowei Chen & Wing Fung Chong & Runhuan Feng & Linfeng Zhang, 2020. "Pandemic risk management: resources contingency planning and allocation," Papers 2012.03200, arXiv.org.
    7. Embrechts, Paul & Puccetti, Giovanni & Rüschendorf, Ludger, 2013. "Model uncertainty and VaR aggregation," Journal of Banking & Finance, Elsevier, vol. 37(8), pages 2750-2764.
    8. 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.
    9. Dietmar Pfeifer & Doreen Strassburger, 2008. "Solvency II: stability problems with the SCR aggregation formula," Scandinavian Actuarial Journal, Taylor & Francis Journals, vol. 2008(4), pages 315-315.
    10. Bølviken, Erik & Guillen, Montserrat, 2017. "Risk aggregation in Solvency II through recursive log-normals," Insurance: Mathematics and Economics, Elsevier, vol. 73(C), pages 20-26.
    11. Francesca Biagini & Jean‐Pierre Fouque & Marco Frittelli & Thilo Meyer‐Brandis, 2019. "A unified approach to systemic risk measures via acceptance sets," Mathematical Finance, Wiley Blackwell, vol. 29(1), pages 329-367, January.
    12. Kang, Woo-Young & Poshakwale, Sunil, 2019. "A new approach to optimal capital allocation for RORAC maximization in banks," Journal of Banking & Finance, Elsevier, vol. 106(C), pages 153-165.
    13. Filipović, Damir, 2009. "Multi-Level Risk Aggregation," ASTIN Bulletin, Cambridge University Press, vol. 39(2), pages 565-575, November.
    14. 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.
    15. Michael Powers, 2007. "Using Aumann-Shapley Values to Allocate Insurance Risk," North American Actuarial Journal, Taylor & Francis Journals, vol. 11(3), pages 113-127.
    16. Arbenz, Philipp & Hummel, Christoph & Mainik, Georg, 2012. "Copula based hierarchical risk aggregation through sample reordering," Insurance: Mathematics and Economics, Elsevier, vol. 51(1), pages 122-133.
    17. Michael Kalkbrener, 2005. "An Axiomatic Approach To Capital Allocation," Mathematical Finance, Wiley Blackwell, vol. 15(3), pages 425-437, July.
    18. Boonen, Tim J. & Tsanakas, Andreas & Wüthrich, Mario V., 2017. "Capital allocation for portfolios with non-linear risk aggregation," Insurance: Mathematics and Economics, Elsevier, vol. 72(C), pages 95-106.
    19. Heilmann, Wolf-Rudiger, 1989. "Decision theoretic foundations of credibility theory," Insurance: Mathematics and Economics, Elsevier, vol. 8(1), pages 77-95, March.
    20. Furman, Edward & Hackmann, Daniel & Kuznetsov, Alexey, 2020. "On log-normal convolutions: An analytical–numerical method with applications to economic capital determination," Insurance: Mathematics and Economics, Elsevier, vol. 90(C), pages 120-134.
    21. 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, March.
    22. Alexander J. McNeil & Rüdiger Frey & Paul Embrechts, 2015. "Quantitative Risk Management: Concepts, Techniques and Tools Revised edition," Economics Books, Princeton University Press, edition 2, number 10496.
    23. Vali Asimit & Liang Peng & Ruodu Wang & Alex Yu, 2019. "An efficient approach to quantile capital allocation and sensitivity analysis," Mathematical Finance, Wiley Blackwell, vol. 29(4), pages 1131-1156, October.
    24. Daniel Bauer & George Zanjani, 2016. "The Marginal Cost of Risk, Risk Measures, and Capital Allocation," Management Science, INFORMS, vol. 62(5), pages 1431-1457, May.
    25. Buch, A. & Dorfleitner, G., 2008. "Coherent risk measures, coherent capital allocations and the gradient allocation principle," Insurance: Mathematics and Economics, Elsevier, vol. 42(1), pages 235-242, February.
    26. Bernard, Carole & Jiang, Xiao & Wang, Ruodu, 2014. "Risk aggregation with dependence uncertainty," Insurance: Mathematics and Economics, Elsevier, vol. 54(C), pages 93-108.
    27. Sarabia, José María & Gómez-Déniz, Emilio & Prieto, Faustino & Jordá, Vanesa, 2016. "Risk aggregation in multivariate dependent Pareto distributions," Insurance: Mathematics and Economics, Elsevier, vol. 71(C), pages 154-163.
    28. Dietmar Pfeifer & Doreen Strassburger, 2008. "Solvency II: stability problems with the SCR aggregation formula," Scandinavian Actuarial Journal, Taylor & Francis Journals, vol. 2008(1), pages 61-77.
    29. Furman, Edward & Zitikis, Ricardas, 2008. "Weighted risk capital allocations," Insurance: Mathematics and Economics, Elsevier, vol. 43(2), pages 263-269, October.
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