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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.

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Article provided by Elsevier in its journal Economic Modelling.

Volume (Year): 29 (2012)
Issue (Month): 4 ()
Pages: 1126-1136

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Handle: RePEc:eee:ecmode:v:29:y:2012:i:4:p:1126-1136
Contact details of provider: Web page: http://www.elsevier.com/locate/inca/30411

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  1. 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, 09.
  2. Jun Liu, 2007. "Portfolio Selection in Stochastic Environments," Review of Financial Studies, Society for Financial Studies, vol. 20(1), pages 1-39, January.
  3. Robert J. Elliott & John van der Hoek, 2001. "Stochastic flows and the forward measure," Finance and Stochastics, Springer, vol. 5(4), pages 511-525.
  4. 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.
  5. Harry Markowitz, 1952. "Portfolio Selection," Journal of Finance, American Finance Association, vol. 7(1), pages 77-91, 03.
  6. 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.
  7. Tao Pang, 2006. "Stochastic Portfolio Optimization With Log Utility," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 9(06), pages 869-887.
  8. 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.
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