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Solvency, Capital Allocation, and Fair Rate of Return in Insurance

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  • Michael Sherris

Abstract

In this article, we consider the links between solvency, capital allocation, and fair rate of return in insurance. A method to allocate capital in insurance to lines of business is developed based on an economic definition of solvency and the market value of the insurer balance sheet. Solvency, and its financial impact, is determined by the value of the insolvency exchange option. The allocation of capital is determined using a complete markets’ arbitrage‐free model and, as a result, has desirable properties, such as the allocated capital “adds up” and is consistent with the economic value of the balance sheet assets and liabilities. A single‐period discrete‐state model example is used to illustrate the results. The impact of adding lines of business is briefly considered.

Suggested Citation

  • Michael Sherris, 2006. "Solvency, Capital Allocation, and Fair Rate of Return in Insurance," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 73(1), pages 71-96, March.
    • Handle: RePEc:bla:jrinsu:v:73:y:2006:i:1:p:71-96
    DOI: 10.1111/j.1365-2966.2006.00166.x
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    Cited by:

    1. John A. Major & Stephen J. Mildenhall, 2020. "Pricing and Capital Allocation for Multiline Insurance Firms With Finite Assets in an Imperfect Market," Papers 2008.12427, arXiv.org.
    2. Huang, Hong-Chih & Lee, Yung-Tsung, 2010. "Optimal asset allocation for a general portfolio of life insurance policies," Insurance: Mathematics and Economics, Elsevier, vol. 46(2), pages 271-280, April.
    3. Li Zhang & Norma Nielson, 2012. "Pricing for Multiline Insurer: Frictional Costs, Insolvency, and Asset Allocation," Risk Management and Insurance Review, American Risk and Insurance Association, vol. 15(2), pages 129-152, September.
    4. Hong‐Chih Huang, 2010. "Optimal Multiperiod Asset Allocation: Matching Assets to Liabilities in a Discrete Model," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 77(2), pages 451-472, June.
    5. George Zanjani, 2010. "An Economic Approach to Capital Allocation," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 77(3), pages 523-549, September.
    6. Dionne, Georges & Harrington, Scott, 2017. "Insurance and Insurance Markets," Working Papers 17-2, HEC Montreal, Canada Research Chair in Risk Management.
    7. Dóra Balog, 2017. "Capital Allocation in the Insurance Sector," Financial and Economic Review, Magyar Nemzeti Bank (Central Bank of Hungary), vol. 16(3), pages 74-97.
    8. Gatzert, Nadine & Schmeiser, Hato, 2008. "Combining fair pricing and capital requirements for non-life insurance companies," Journal of Banking & Finance, Elsevier, vol. 32(12), pages 2589-2596, December.
    9. Bilel Jarraya & Abdelfettah Bouri, 2013. "A Theoretical Assessment on Optimal Asset Allocations in Insurance Industry," International Journal of Finance & Banking Studies, Center for the Strategic Studies in Business and Finance, vol. 2(4), pages 30-44, October.
    10. van Gulick, Gerwald & De Waegenaere, Anja & Norde, Henk, 2012. "Excess based allocation of risk capital," Insurance: Mathematics and Economics, Elsevier, vol. 50(1), pages 26-42.
    11. Mao Hong & Carson James M. & Ostaszewski Krzysztof M., 2018. "Optimal Price Setting and Insurer Capital Management in a Multiple Line Context," Asia-Pacific Journal of Risk and Insurance, De Gruyter, vol. 12(1), pages 1-22, January.
    12. Robin Chark & Vincent Mak & A. V. Muthukrishnan, 2020. "The premium as informational cue in insurance decision making," Theory and Decision, Springer, vol. 88(3), pages 369-404, April.
    13. Gatzert, Nadine & Schmeiser, Hato, 2008. "The influence of corporate taxes on pricing and capital structure in property-liability insurance," Insurance: Mathematics and Economics, Elsevier, vol. 42(1), pages 50-58, February.
    14. Hato Schmeiser & Joël Wagner, 2013. "The Impact of Introducing Insurance Guaranty Schemes on Pricing and Capital Structure," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 80(2), pages 273-308, June.
    15. Wang, Wei & Xu, Huifu & Ma, Tiejun, 2023. "Optimal scenario-dependent multivariate shortfall risk measure and its application in risk capital allocation," European Journal of Operational Research, Elsevier, vol. 306(1), pages 322-347.
    16. 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.
    17. 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.
    18. Kim, Joseph H.T. & Hardy, Mary R., 2009. "A capital allocation based on a solvency exchange option," Insurance: Mathematics and Economics, Elsevier, vol. 44(3), pages 357-366, June.
    19. Boonen, Tim J., 2019. "Equilibrium recoveries in insurance markets with limited liability," Journal of Mathematical Economics, Elsevier, vol. 85(C), pages 38-45.
    20. van Gulick, G. & De Waegenaere, A.M.B. & Norde, H.W., 2010. "Excess Based Allocation of Risk Capital," Other publications TiSEM f9231521-fea7-4524-8fea-8, Tilburg University, School of Economics and Management.
    21. Stephen J. Mildenhall, 2017. "Actuarial Geometry," Risks, MDPI, vol. 5(2), pages 1-44, June.
    22. Mélina Mailhot & Mhamed Mesfioui, 2016. "Multivariate TVaR-Based Risk Decomposition for Vector-Valued Portfolios," Risks, MDPI, vol. 4(4), pages 1-16, September.
    23. Schlütter, Sebastian, 2011. "Capital requirements or pricing constraints? An economic analysis of measures for insurance regulation," ICIR Working Paper Series 03/11, Goethe University Frankfurt, International Center for Insurance Regulation (ICIR).
    24. Lee, Hangsuck & Choi, Hyung-Suk & Ha, Hongjun, 2020. "A sharing mechanism of investment outcome for interest-sensitive life insurance products," The North American Journal of Economics and Finance, Elsevier, vol. 54(C).
    25. Jean-François Outreville, 2014. "The Meaning of Risk? Insights from The Geneva Risk and Insurance Review," The Geneva Papers on Risk and Insurance - Issues and Practice, Palgrave Macmillan;The Geneva Association, vol. 39(4), pages 768-781, October.

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