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Pension funding problem with regime‐switching geometric Brownian motion assets and liabilities

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  • Ping Chen
  • Hailiang Yang

Abstract

This paper extends the pension funding model in (N. Am. Actuarial J. 2003; 7:37–51) to a regime‐switching case. The market mode is modeled by a continuous‐time stationary Markov chain. The asset value process and liability value process are modeled by Markov‐modulated geometric Brownian motions. We consider a pension funding plan in which the asset value is to be within a band that is proportional to the liability value. The pension plan sponsor is asked to provide sufficient funds to guarantee the asset value stays above the lower barrier of the band. The amount by which the asset value exceeds the upper barrier will be paid back to the sponsor. By applying differential equation approach, this paper calculates the expected present value of the payments to be made by the sponsor as well as that of the refunds to the sponsor. In addition, we study the effects of different barriers and regime switching on the results using some numerical examples. The optimal dividend problem is studied in our examples as an application of our theory. Copyright © 2009 John Wiley & Sons, Ltd.

Suggested Citation

  • Ping Chen & Hailiang Yang, 2010. "Pension funding problem with regime‐switching geometric Brownian motion assets and liabilities," Applied Stochastic Models in Business and Industry, John Wiley & Sons, vol. 26(2), pages 125-141, March.
    • Handle: RePEc:wly:apsmbi:v:26:y:2010:i:2:p:125-141
    DOI: 10.1002/asmb.776
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    References listed on IDEAS

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    1. Hans Gerber & Elias Shiu, 2003. "Geometric Brownian Motion Models for Assets and Liabilities: From Pension Funding to Optimal Dividends," North American Actuarial Journal, Taylor & Francis Journals, vol. 7(3), pages 37-51.
    2. Boyle, Phelim & Draviam, Thangaraj, 2007. "Pricing exotic options under regime switching," Insurance: Mathematics and Economics, Elsevier, vol. 40(2), pages 267-282, March.
    3. John Buffington & Robert J. Elliott, 2002. "American Options With Regime Switching," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 5(05), pages 497-514.
    4. Asmussen, Soren & Taksar, Michael, 1997. "Controlled diffusion models for optimal dividend pay-out," Insurance: Mathematics and Economics, Elsevier, vol. 20(1), pages 1-15, June.
    5. Town, R J, 1992. "Merger Waves and the Structure of Merger and Acquisition Time-Series," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 7(S), pages 83-100, Suppl. De.
    6. Mary Hardy, 2001. "A Regime-Switching Model of Long-Term Stock Returns," North American Actuarial Journal, Taylor & Francis Journals, vol. 5(2), pages 41-53.
    7. Paul Storer & Marc A. Van Audenrode, 1995. "Unemployment Insurance Take-Up Rates in Canada: Facts, Determinants, and Implications," Canadian Journal of Economics, Canadian Economics Association, vol. 28(4a), pages 822-835, November.
    8. Shuanming Li & Yi Lu, 2007. "Moments of the Dividend Payments and Related Problems in a Markov-Modulated Risk Model," North American Actuarial Journal, Taylor & Francis Journals, vol. 11(2), pages 65-76.
    9. Hans U. Gerber, 1972. "Games of Economic Survival with Discrete- and Continuous-Income Processes," Operations Research, INFORMS, vol. 20(1), pages 37-45, February.
    10. Hans Gerber & Elias Shiu, 1998. "On the Time Value of Ruin," North American Actuarial Journal, Taylor & Francis Journals, vol. 2(1), pages 48-72.
    11. Bjarne Hø Jgaard & Michael Taksar, 1999. "Controlling Risk Exposure and Dividends Payout Schemes:Insurance Company Example," Mathematical Finance, Wiley Blackwell, vol. 9(2), pages 153-182, April.
    12. Hamilton, James D, 1989. "A New Approach to the Economic Analysis of Nonstationary Time Series and the Business Cycle," Econometrica, Econometric Society, vol. 57(2), pages 357-384, March.
    13. Robert Elliott & Tak Kuen Siu, 2009. "On Markov-modulated Exponential-affine Bond Price Formulae," Applied Mathematical Finance, Taylor & Francis Journals, vol. 16(1), pages 1-15.
    14. Raymond, Jennie E & Rich, Robert W, 1997. "Erratum [Oil and the Macroeconomy: A Markov State-Switching Approach]," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 29(4), pages 555-555, November.
    15. Chen, Ping & Yang, Hailiang & Yin, George, 2008. "Markowitz's mean-variance asset-liability management with regime switching: A continuous-time model," Insurance: Mathematics and Economics, Elsevier, vol. 43(3), pages 456-465, December.
    16. Neftci, Salih N, 1984. "Are Economic Time Series Asymmetric over the Business Cycle?," Journal of Political Economy, University of Chicago Press, vol. 92(2), pages 307-328, April.
    17. Chang-Jin Kim & Charles R. Nelson, 1999. "State-Space Models with Regime Switching: Classical and Gibbs-Sampling Approaches with Applications," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262112388, December.
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