IDEAS home Printed from https://ideas.repec.org/a/wly/apsmbi/v26y2010i2p125-141.html
   My bibliography  Save this article

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

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: https://doi.org/10.1002/asmb.776
    Download Restriction: no
    File URL: https://libkey.io/10.1002/asmb.776?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. 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. "Oil and the Macroeconomy: A Markov State-Switching Approach," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 29(2), pages 193-213, May.
    15. 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.
    16. 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.
    17. 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.
    18. 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, April.
    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. Chen, Ping & Yam, S.C.P., 2013. "Optimal proportional reinsurance and investment with regime-switching for mean–variance insurers," Insurance: Mathematics and Economics, Elsevier, vol. 53(3), pages 871-883.
    2. Meng, Hui & Siu, Tak Kuen, 2011. "On optimal reinsurance, dividend and reinvestment strategies," Economic Modelling, Elsevier, vol. 28(1-2), pages 211-218, January.
    3. Godin, Frédéric & Lai, Van Son & Trottier, Denis-Alexandre, 2019. "Option pricing under regime-switching models: Novel approaches removing path-dependence," Insurance: Mathematics and Economics, Elsevier, vol. 87(C), pages 130-142.
    4. Alessandro Ramponi, 2011. "Mixture Dynamics and Regime Switching Diffusions with Application to Option Pricing," Methodology and Computing in Applied Probability, Springer, vol. 13(2), pages 349-368, June.
    5. Yuen, Kam C. & Wang, Guojing & Li, Wai K., 2007. "The Gerber-Shiu expected discounted penalty function for risk processes with interest and a constant dividend barrier," Insurance: Mathematics and Economics, Elsevier, vol. 40(1), pages 104-112, January.
    6. Zhengjun Jiang & Martijn Pistorius, 2012. "Optimal dividend distribution under Markov regime switching," Finance and Stochastics, Springer, vol. 16(3), pages 449-476, July.
    7. Emilio Russo, 2020. "A Discrete-Time Approach to Evaluate Path-Dependent Derivatives in a Regime-Switching Risk Model," Risks, MDPI, vol. 8(1), pages 1-22, January.
    8. Godin, Frédéric & Trottier, Denis-Alexandre, 2021. "Option pricing in regime-switching frameworks with the Extended Girsanov Principle," Insurance: Mathematics and Economics, Elsevier, vol. 99(C), pages 116-129.
    9. Massimo Costabile & Arturo Leccadito & Ivar Massabó & Emilio Russo, 2014. "A reduced lattice model for option pricing under regime-switching," Review of Quantitative Finance and Accounting, Springer, vol. 42(4), pages 667-690, May.
    10. Fan, Kun & Shen, Yang & Siu, Tak Kuen & Wang, Rongming, 2015. "Valuing commodity options and futures options with changing economic conditions," Economic Modelling, Elsevier, vol. 51(C), pages 524-533.
    11. Guan, Huiqi & Liang, Zongxia, 2014. "Viscosity solution and impulse control of the diffusion model with reinsurance and fixed transaction costs," Insurance: Mathematics and Economics, Elsevier, vol. 54(C), pages 109-122.
    12. Peter Hieber, 2018. "Pricing exotic options in a regime switching economy: a Fourier transform method," Review of Derivatives Research, Springer, vol. 21(2), pages 231-252, July.
    13. Andreopoulos Spyros, 2009. "Oil Matters: Real Input Prices and U.S. Unemployment Revisited," The B.E. Journal of Macroeconomics, De Gruyter, vol. 9(1), pages 1-31, March.
    14. Gao, Huan & Mamon, Rogemar & Liu, Xiaoming & Tenyakov, Anton, 2015. "Mortality modelling with regime-switching for the valuation of a guaranteed annuity option," Insurance: Mathematics and Economics, Elsevier, vol. 63(C), pages 108-120.
    15. Beckmann, Joscha & Czudaj, Robert, 2013. "Is there a homogeneous causality pattern between oil prices and currencies of oil importers and exporters?," Energy Economics, Elsevier, vol. 40(C), pages 665-678.
    16. Oleg Korenok & Bruce Mizrach, 2004. "The Microeconomics of Macroeconomic Asymmetries: Sectoral Driving Forces and Firm Level Characteristics," Computing in Economics and Finance 2004 266, Society for Computational Economics.
    17. Taylor, Andrew & Shepherd, David & Duncan, Stephen, 2005. "The structure of the Australian growth process: A Bayesian model selection view of Markov switching," Economic Modelling, Elsevier, vol. 22(4), pages 628-645, July.
    18. Sinclair Tara M, 2009. "Asymmetry in the Business Cycle: Friedman's Plucking Model with Correlated Innovations," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 14(1), pages 1-31, December.
    19. Zhou, Zhou & Jin, Zhuo, 2020. "Optimal equilibrium barrier strategies for time-inconsistent dividend problems in discrete time," Insurance: Mathematics and Economics, Elsevier, vol. 94(C), pages 100-108.
    20. Charles Nelson & Jeremy Piger & Eric Zivot, 1999. "Unit Root Tests in the Presence of Markov Regime-Switching," Discussion Papers in Economics at the University of Washington 0040, Department of Economics at the University of Washington.

    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:wly:apsmbi:v:26:y:2010:i:2:p:125-141. 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: https://doi.org/10.1002/(ISSN)1526-4025 .

    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.