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The Distributions of Policy Reserves Considering the Policy‐Year Structures of Surrender Rates and Expense Ratios

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  • Chenghsien Tsai
  • Weiyu Kuo
  • Derek Mi‐Hsiu Chiang

Abstract

In this article, we examine how the policy‐year structures of expense ratios and surrender rates affect the distributions of policy reserves. Our results show that a convex expense ratio curve, though reduces the mean and the uncertainty of reserves, could make the beneficial impact of surrenders on insurers become detrimental. Our results also show that the convexity of the surrender rate curve is favorable to insurers while the volatilities of surrender rates are unfavorable. We further find that neglecting the policy‐year structures of surrender rates and expense ratios may result in overestimation of the mean and the uncertainty of reserves.

Suggested Citation

  • Chenghsien Tsai & Weiyu Kuo & Derek Mi‐Hsiu Chiang, 2009. "The Distributions of Policy Reserves Considering the Policy‐Year Structures of Surrender Rates and Expense Ratios," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 76(4), pages 909-931, December.
    • Handle: RePEc:bla:jrinsu:v:76:y:2009:i:4:p:909-931
    DOI: 10.1111/j.1539-6975.2009.01324.x
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    References listed on IDEAS

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    1. David Babbel & Craig Merrill, 1998. "Economic Valuation Models for Insurers," North American Actuarial Journal, Taylor & Francis Journals, vol. 2(3), pages 1-15.
    2. David Babbel & Jeremy Gold & Craig Merrill, 2002. "Fair Value of Liabilities: The Financial Economics Perspective," North American Actuarial Journal, Taylor & Francis Journals, vol. 6(1), pages 12-27.
    3. Beekman, John A. & Fuelling, Clinton P., 1990. "Interest and mortality randomness in some annuities," Insurance: Mathematics and Economics, Elsevier, vol. 9(2-3), pages 185-196, September.
    4. Marceau, Etienne & Gaillardetz, Patrice, 1999. "On life insurance reserves in a stochastic mortality and interest rates environment," Insurance: Mathematics and Economics, Elsevier, vol. 25(3), pages 261-280, December.
    5. Parker, Gary, 1994. "Limiting Distribution of the Present Value of a Portfolio," ASTIN Bulletin, Cambridge University Press, vol. 24(1), pages 47-60, May.
    6. Parker, Gary, 1996. "A portfolio of endowment policies and its limiting distribution," ASTIN Bulletin, Cambridge University Press, vol. 26(1), pages 25-33, May.
    7. Tsai, Chenghsien & Kuo, Weiyu & Chen, Wei-Kuang, 2002. "Early surrender and the distribution of policy reserves," Insurance: Mathematics and Economics, Elsevier, vol. 31(3), pages 429-445, December.
    8. De Schepper, A. & Goovaerts, M., 1992. "Some further results on annuities certain with random interest," Insurance: Mathematics and Economics, Elsevier, vol. 11(4), pages 283-290, December.
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    Cited by:

    1. Martin Eling & Michael Kochanski, 2013. "Research on lapse in life insurance: what has been done and what needs to be done?," Journal of Risk Finance, Emerald Group Publishing Limited, vol. 14(4), pages 392-413, August.

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