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Limiting Distribution of the Present Value of a Portfolio

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  • Parker, Gary

Abstract

An approximation of the distribution of the present value of the benefits of a portfolio of temporary insurance contracts is suggested for the case where the size of the portfolio tends to infinity. The model used is the one presented in Parker (1922b) and involves random interest rates and future lifetimes. Some justifications of the approximation are given. Illustrations for limiting portfolios of temporary insurance contracts are presented for an assumed Ornstein-Uhlenbeck process for the force of interest.

Suggested Citation

  • Parker, Gary, 1994. "Limiting Distribution of the Present Value of a Portfolio," ASTIN Bulletin, Cambridge University Press, vol. 24(1), pages 47-60, May.
    • Handle: RePEc:cup:astinb:v:24:y:1994:i:01:p:47-60_00
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    Citations

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    Cited by:

    1. Nolde, Natalia & Parker, Gary, 2014. "Stochastic analysis of life insurance surplus," Insurance: Mathematics and Economics, Elsevier, vol. 56(C), pages 1-13.
    2. 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.
    3. Chen, Li & Lin, Luyao & Lu, Yi & Parker, Gary, 2017. "Analysis of survivorship life insurance portfolios with stochastic rates of return," Insurance: Mathematics and Economics, Elsevier, vol. 75(C), pages 16-31.
    4. Xia Zhao & Bo Zhang, 2012. "Pricing perpetual options with stochastic discount interest rates," Quality & Quantity: International Journal of Methodology, Springer, vol. 46(1), pages 341-349, January.
    5. 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.
    6. Debicka, Joanna, 2003. "Moments of the cash value of future payment streams arising from life insurance contracts," Insurance: Mathematics and Economics, Elsevier, vol. 33(3), pages 533-550, December.
    7. Constantinos T. Artikis, 2012. "Formulating a Stochastic Discounting Model with Actuarial and Risk Management Applications," SPOUDAI Journal of Economics and Business, SPOUDAI Journal of Economics and Business, University of Piraeus, vol. 62(3-4), pages 7-15, July - De.
    8. Parker, Gary, 1995. "A second order stochastic differential equation for the force of interest," Insurance: Mathematics and Economics, Elsevier, vol. 16(3), pages 211-224, July.
    9. Cairns, Andrew J. G. & Parker, Gary, 1997. "Stochastic pension fund modelling," Insurance: Mathematics and Economics, Elsevier, vol. 21(1), pages 43-79, October.
    10. Hoedemakers, Tom & Darkiewicz, Grzegorz & Goovaerts, Marc, 2005. "Approximations for life annuity contracts in a stochastic financial environment," Insurance: Mathematics and Economics, Elsevier, vol. 37(2), pages 239-269, October.
    11. 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.
    12. Cocozza, Rosa & Di Lorenzo, Emilia, 2007. "A Dynamic Solvency Approach for Life Insurance," MPRA Paper 28015, University Library of Munich, Germany.
    13. Maria Gota, 1996. "Modelli multistato per le assicurazioni di persone: approccio stocastico all'analisi dell'utile con procedimenti simulativi," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 19(1), pages 39-52, March.

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