IDEAS home Printed from https://ideas.repec.org/a/bla/rmgtin/v15y2012i2p129-152.html
   My bibliography  Save this article

Pricing for Multiline Insurer: Frictional Costs, Insolvency, and Asset Allocation

Author

Listed:
  • Li Zhang
  • Norma Nielson

Abstract

This article examines multiline insurance pricing based on the contingent claim approach in a limited liability and frictional costs environment. Capital allocation is based on the value of the default option, which satisfies the realistic assumption that each distinct line undertakes a pro rata share of deficit caused by insurer insolvency. Premium levels, available assets, and default risk interact with each other and reach equilibrium at the fair premium. The assets available to pay for liabilities are not predetermined or given; instead, the premium income and investment income jointly influence the available assets. The results show that equity allocation does not influence the overall fair premium. For a given expected loss, the premium‐to‐expected‐loss ratio for firms offering multiple lines is higher than that for firms only offering a single line, due to the reduced risk achieved through diversification. Premium‐to‐expected‐loss ratio and equity‐to‐expected‐loss ratio vary across lines. Lines having a higher possibility or claim amount not being paid in full exhibit lower premium‐to‐expected‐loss ratio and higher equity‐to‐expected‐loss ratio. Positive correlation among lines of business results in lower premium‐to‐expected‐loss ratio than when independent losses are assumed. Positive correlation between investment return and losses reduces the insolvency risk and leads to a higher premium‐to‐expected‐loss ratio.

Suggested Citation

  • 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.
    • Handle: RePEc:bla:rmgtin:v:15:y:2012:i:2:p:129-152
    DOI: j.1540-6296.2012.01214.x
    as

    Download full text from publisher

    File URL: https://doi.org/10.1111/j.1540-6296.2012.01214.x
    Download Restriction: no
    File URL: https://libkey.io/j.1540-6296.2012.01214.x?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    References listed on IDEAS

    as
    1. Rustam Ibragimov & Dwight Jaffee & Johan Walden, 2010. "Pricing and Capital Allocation for Multiline Insurance Firms," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 77(3), pages 551-578, September.
    2. 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.
    3. Jorge Urrutia, 1987. "Determination of Competitive Underwriting Profit Margins Using Arbitrage Pricing Theory Model," Journal of Insurance Issues, Western Risk and Insurance Association, vol. 10(2), pages 61-77.
    4. Doherty, Neil A & Garven, James R, 1986. "Price Regulation in Property-Liability Insurance: A Contingent-Claims Approach," Journal of Finance, American Finance Association, vol. 41(5), pages 1031-1050, December.
    5. Raymond D. Hill, 1979. "Profit Regulation in Property-Liability Insurance," Bell Journal of Economics, The RAND Corporation, vol. 10(1), pages 172-191, Spring.
    6. Merton, Robert C., 1977. "An analytic derivation of the cost of deposit insurance and loan guarantees An application of modern option pricing theory," Journal of Banking & Finance, Elsevier, vol. 1(1), pages 3-11, June.
    7. Kraus, Alan & Ross, Stephen A, 1982. "The Determination of Fair Profits for the Property-Liability Insurance Firm," Journal of Finance, American Finance Association, vol. 37(4), pages 1015-1028, September.
    8. William B. Fairley, 1979. "Investment Income and Profit Margins in Property-Liability Insurance: Theory and Empirical Results," Bell Journal of Economics, The RAND Corporation, vol. 10(1), pages 192-210, Spring.
    9. Lo, Andrew W., 1987. "Semi-parametric upper bounds for option prices and expected payoffs," Journal of Financial Economics, Elsevier, vol. 19(2), pages 373-387, December.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Dionne, Georges & Harrington, Scott, 2017. "Insurance and Insurance Markets," Working Papers 17-2, HEC Montreal, Canada Research Chair in Risk Management.
    2. Lim, Terence & Lo, Andrew W. & Merton, Robert C. & Scholes, Myron S., 2006. "The Derivatives Sourcebook," Foundations and Trends(R) in Finance, now publishers, vol. 1(5–6), pages 365-572, April.
    3. Henri Loubergé, 1998. "Risk and Insurance Economics 25 Years After," The Geneva Papers on Risk and Insurance - Issues and Practice, Palgrave Macmillan;The Geneva Association, vol. 23(4), pages 540-567, October.
    4. Yueyun Chen & Iskandar Hamwi & Tim Hudson, 2003. "Capital asset pricing models with default risk: Theory and application in insurance," International Advances in Economic Research, Springer;International Atlantic Economic Society, vol. 9(1), pages 20-34, February.
    5. Garven, James R. & Louberge, Henri, 1996. "Reinsurance, Taxes, and Efficiency: A Contingent Claims Model of Insurance Market Equilibrium," Journal of Financial Intermediation, Elsevier, vol. 5(1), pages 74-93, January.
    6. 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.
    7. Cummins, J. David & Danzon, Patricia M., 1997. "Price, Financial Quality, and Capital Flows in Insurance Markets," Journal of Financial Intermediation, Elsevier, vol. 6(1), pages 3-38, January.
    8. Richard D. Phillips & J. David Cummins & Franklin Allen, 1996. "Financial Pricing of Insurance in the Multiple Line Insurance Company," Center for Financial Institutions Working Papers 96-09, Wharton School Center for Financial Institutions, University of Pennsylvania.
    9. 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.
    10. Anne Gron & Deborah J. Lucas, 1998. "External Financing and Insurance Cycles," NBER Chapters, in: The Economics of Property-Casualty Insurance, pages 5-28, National Bureau of Economic Research, Inc.
    11. Boonen, Tim J., 2019. "Equilibrium recoveries in insurance markets with limited liability," Journal of Mathematical Economics, Elsevier, vol. 85(C), pages 38-45.
    12. Eling, Martin & Jia, Ruo & Schaper, Philipp, 2017. "Get the Balance Right: A Simultaneous Equation Model to Analyze Growth, Profitability, and Safety," Working Papers on Finance 1716, University of St. Gallen, School of Finance.
    13. Lai, Li-Hua, 2008. "An evaluation of fuzzy transportation underwriting systematic risk," Transportation Research Part A: Policy and Practice, Elsevier, vol. 42(9), pages 1231-1237, November.
    14. Li-Hua Lai, 2006. "Underwriting profit margin of P/L insurance in the fuzzy-ICAPM," The Geneva Papers on Risk and Insurance Theory, Springer;International Association for the Study of Insurance Economics (The Geneva Association), vol. 31(1), pages 23-34, July.
    15. Ligon, James A. & Cather, David A., 1997. "The informational value of insurance purchases: Evidence from the property-liability insurance market," Journal of Banking & Finance, Elsevier, vol. 21(7), pages 989-1016, July.
    16. Stephen J. Mildenhall, 2017. "Actuarial Geometry," Risks, MDPI, vol. 5(2), pages 1-44, June.
    17. Jeffrey I. Bernstein, 1992. "Information Spillovers, Margins, Scale and Scope: With an Application to Canadian Life Insurance," NBER Working Papers 3979, National Bureau of Economic Research, Inc.
    18. 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.
    19. Martin Eling, 2012. "What Do We Know About Market Discipline in Insurance?," Risk Management and Insurance Review, American Risk and Insurance Association, vol. 15(2), pages 185-223, September.
    20. Fred Lazar & Eliezer Z. Prisman, 2015. "Regulator's Determination of Return on Equity in the Absence of Public Firms: The Case of Automobile Insurance in Ontario," Risk Management and Insurance Review, American Risk and Insurance Association, vol. 18(2), pages 199-216, September.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:bla:rmgtin:v:15:y:2012:i:2:p:129-152. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Wiley Content Delivery (email available below). General contact details of provider: http://www.blackwellpublishing.com/journal.asp?ref=1098-1616 .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.