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Asset allocation under stochastic interest rate with regime switching


  • Shen, Yang
  • Siu, Tak Kuen


We investigate an optimal asset allocation problem in a Markovian regime-switching financial market with stochastic interest rate. The market has three investment opportunities, namely, a bank account, a share and a zero-coupon bond, where stochastic movements of the short rate and the share price are governed by a Markovian regime-switching Vasicek model and a Markovian regime-switching Geometric Brownian motion, respectively. We discuss the optimal asset allocation problem using the dynamic programming approach for stochastic optimal control and derive a regime-switching Hamilton–Jacobi–Bellman (HJB) equation. Particular attention is paid to the exponential utility case. Numerical and sensitivity analysis are provided for this case. The numerical results reveal that regime-switches described by a two-state Markov chain have significant impacts on the optimal investment strategies in the share and the bond. Furthermore, the market prices of risk in both the bond and share markets are crucial factors in determining the optimal investment strategies.

Suggested Citation

  • Shen, Yang & Siu, Tak Kuen, 2012. "Asset allocation under stochastic interest rate with regime switching," Economic Modelling, Elsevier, vol. 29(4), pages 1126-1136.
  • Handle: RePEc:eee:ecmode:v:29:y:2012:i:4:p:1126-1136 DOI: 10.1016/j.econmod.2012.03.024

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    References listed on IDEAS

    1. Jérˆme Detemple & Marcel Rindisbacher, 2005. "Closed-Form Solutions For Optimal Portfolio Selection With Stochastic Interest Rate And Investment Constraints," Mathematical Finance, Wiley Blackwell, vol. 15(4), pages 539-568.
    2. 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.
    3. Lioui, Abraham & Poncet, Patrice, 2001. "On optimal portfolio choice under stochastic interest rates," Journal of Economic Dynamics and Control, Elsevier, vol. 25(11), pages 1841-1865, November.
    4. Robert J. Elliott & John van der Hoek, 2001. "Stochastic flows and the forward measure," Finance and Stochastics, Springer, vol. 5(4), pages 511-525.
    5. Harry Markowitz, 1952. "Portfolio Selection," Journal of Finance, American Finance Association, vol. 7(1), pages 77-91, March.
    6. William F. Sharpe, 1964. "Capital Asset Prices: A Theory Of Market Equilibrium Under Conditions Of Risk," Journal of Finance, American Finance Association, vol. 19(3), pages 425-442, September.
    7. Jun Liu, 2007. "Portfolio Selection in Stochastic Environments," Review of Financial Studies, Society for Financial Studies, vol. 20(1), pages 1-39, January.
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    Cited by:

    1. repec:eee:ecmode:v:66:y:2017:i:c:p:223-232 is not listed on IDEAS
    2. Jinzhi Li & Haiying Liu, 2015. "Optimal Investment for the Insurers in Markov-Modulated Jump-Diffusion Models," Computational Economics, Springer;Society for Computational Economics, vol. 46(1), pages 143-156, June.
    3. Yao, Haixiang & Li, Zhongfei & Li, Duan, 2016. "Multi-period mean-variance portfolio selection with stochastic interest rate and uncontrollable liability," European Journal of Operational Research, Elsevier, vol. 252(3), pages 837-851.
    4. Yao, Haixiang & Chen, Ping & Li, Xun, 2016. "Multi-period defined contribution pension funds investment management with regime-switching and mortality risk," Insurance: Mathematics and Economics, Elsevier, vol. 71(C), pages 103-113.
    5. Nicole Bauerle & Stefanie Grether, 2017. "Extremal Behavior of Long-Term Investors with Power Utility," Papers 1703.04423,, revised Jun 2017.
    6. repec:wsi:ijtafx:v:20:y:2017:i:05:n:s0219024917500297 is not listed on IDEAS
    7. Shen, Yang & Siu, Tak Kuen, 2013. "Pricing bond options under a Markovian regime-switching Hull–White model," Economic Modelling, Elsevier, vol. 30(C), pages 933-940.
    8. Chang, Hao, 2015. "Dynamic mean–variance portfolio selection with liability and stochastic interest rate," Economic Modelling, Elsevier, vol. 51(C), pages 172-182.


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