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Optimal Insurance With Costly Internal Capital

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  • Dwight Jaffee
  • Johan Walden

Abstract

We introduce costly internal capital into a standard insurance model, in which a risk‐averse policyholder buys insurance from a risk‐neutral insurer with limited liability. The unique optimal contract and internal capital lead to a strictly positive probability for insurer default. Some risks are uninsurable in that the insurer chooses not to provide insurance against such risks. An increase in the cost of capital may lead to a higher optimal amount of internal capital. The results extend to multiple policyholders in a symmetric setting. Our extension of the classical model to include costly internal capital provides a fruitful approach to many real world insurance markets.

Suggested Citation

  • Dwight Jaffee & Johan Walden, 2014. "Optimal Insurance With Costly Internal Capital," Risk Management and Insurance Review, American Risk and Insurance Association, vol. 17(2), pages 137-161, September.
    • Handle: RePEc:bla:rmgtin:v:17:y:2014:i:2:p:137-161
    DOI: 10.1111/rmir.12022
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    References listed on IDEAS

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    1. Cummins, J David & Mahul, Olivier, 2003. "Optimal Insurance with Divergent Beliefs about Insurer Total Default Risk," Journal of Risk and Uncertainty, Springer, vol. 27(2), pages 121-138, October.
    2. Gur Huberman & David Mayers & Clifford W. Smith Jr., 1983. "Optimal Insurance Policy Indemnity Schedules," Bell Journal of Economics, The RAND Corporation, vol. 14(2), pages 415-426, Autumn.
    3. J. David Cummins & Olivier Mahul, 2004. "The demand for insurance with an upper limit on coverage," Post-Print hal-01952122, HAL.
    4. J. David Cummins & Olivier Mahul, 2004. "The Demand for Insurance With an Upper Limit on Coverage," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 71(2), pages 253-264, June.
    5. Kenneth A. Froot, 2007. "Risk Management, Capital Budgeting, and Capital Structure Policy for Insurers and Reinsurers," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 74(2), pages 273-299, June.
    6. Neil A. Doherty & Christian Laux & Alexander Muermann, 2015. "Insuring Nonverifiable Losses," Review of Finance, European Finance Association, vol. 19(1), pages 283-316.
    7. Froot, Kenneth A. & Stein, Jeremy C., 1998. "Risk management, capital budgeting, and capital structure policy for financial institutions: an integrated approach," Journal of Financial Economics, Elsevier, vol. 47(1), pages 55-82, January.
    8. Mahul, Olivier & Wright, Brian D., 2007. "Optimal coverage for incompletely reliable insurance," Economics Letters, Elsevier, vol. 95(3), pages 456-461, June.
    9. Neil A. Doherty & Harris Schlesinger, 1990. "Rational Insurance Purchasing: Consideration of Contract Nonperformance," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 105(1), pages 243-253.
    10. Robert C. Merton & André Perold, 1993. "Theory Of Risk Capital In Financial Firms," Journal of Applied Corporate Finance, Morgan Stanley, vol. 6(3), pages 16-32, September.
    11. Froot, Kenneth A & Scharfstein, David S & Stein, Jeremy C, 1993. "Risk Management: Coordinating Corporate Investment and Financing Policies," Journal of Finance, American Finance Association, vol. 48(5), pages 1629-1658, December.
    12. Meyer, Jack & Ormiston, Michael B, 1999. "Analyzing the Demand for Deductible Insurance," Journal of Risk and Uncertainty, Springer, vol. 18(3), pages 223-230, October.
    13. repec:bla:econom:v:71:y:2004:i:284:p:661-670 is not listed on IDEAS
    14. Marek Kaluszka & Andrzej Okolewski, 2008. "An Extension of Arrow's Result on Optimal Reinsurance Contract," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 75(2), pages 275-288, June.
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