Abstract
This paper considers the continuous-time portfolio optimization problem with both stochastic interest rate and stochastic volatility in regime-switching models, where a regime-switching Vasicek model is assumed for the interest rate and a regime-switching Heston model is assumed for the stock price.We use the dynamic programming approach to solve this stochastic optimal control problem. Under suitable assumptions, we prove a verification theorem.We then derive a closed-form solution of the associated Hamilton-Jacobi-Bellman (HJB) equation for a power utility function and a special choice of some model parameters. We prove the optimality of the closed-form solution by verifying the required conditions as stated in the verification theorem. We present a numerical example to show the optimal portfolio policies and value functions in different regimes.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Bansal, R. and Zhou, H. (2002). Term structure of interest rates with regime shifts. Journal of Finance, 57, 1997–2043.
Bäuerle, N. and Rieder, U. (2004). Portfolio optimization with markov-modulated stock prices and interest rates. IEEE Trans. on Auomatic Control, 49(3), 442–447.
Bäuerle, N. and Rieder, U. (2007). Portfolio optimization with jumps and unobservable intensity process. Mathematical Finance, 17(2), 205–224.
Fu, J., Wei, J. and Yang, H. (2014). Portfolio optimization in a regime-switching market with derivatives, European Journal of Operational Research. 233, 184–192.
Hardy, M. (2001). A regime-switching model for long-term stock returns. North American Actuarial Journal, 5, 41–53.
Korn, R. and Kraft, H. (2001). A stochastic control approach to portfolio problems with stochastic interest rates. SIAM J. Control and Optimization, 40(4), 1250–1269.
Kraft, H. (2005). Optimal portfolios and Heston’s stochastic volatility model: an explicit solution for power utility. Quantitative Finance, 5(3), 303–313.
Li, J.Z. and Wu, R. (2009). Optimal investment problem with stochastic interest rate and stochastic volatility:Maximizing a power utility. Appl. Stochastic Models Bus. Ind., 25, 407–420.
Papanicolaou, A. and Sircar, R. (2014). A Regime-switching Heston model for VIX and S&P 500 implied volatilities. Quantitative Finance, 44(10), 1811–1827.
Rieder, U. and Bäuerle, N. (2005). Portfolio optimization with unobservable markovmodulated drift process. Journal of Applied Probability, 42(2), 362–378.
Sass, J. and Haussmann, U. (2004). Optimizing the terminal wealth under partial information: The drift process as a continuous time markov chain. Finance Stochast., 8, 553–577.
Sotomayor, L. and Cadenillas, A. (2009). Explicit solutions of consumption-investment problems in financial markets with regime switching, Mathematical Finance, 19(2), 251–279.
Ye, C., Ren, D. and Liu, R.H. (2018). Optimal asset allocation with stochastic interest rates in regime-switching models. Int. J. Theor. Appl. Finance, 21(5), 1-32. DOI: https://doi.org/10.1142/S0219024918500322.
Yin, G. and Zhang, Q.: Continuous-Time Markov Chains and Applications: A Singular Perturbation Approach. New York, Springer-Verlag (1998)
Zhang, X., Siu, T. andMeng, Q. (2010). Portfolio selection in the enlarged markovian regimeswitching market. SIAM J. Control and Optimization, 48(5), 3368–3388.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2019 Springer Nature Switzerland AG
About this chapter
Cite this chapter
Liu, R.H., Ren, D. (2019). Portfolio Optimization Using Regime-Switching Stochastic Interest Rate and Stochastic Volatility Models. In: Yin, G., Zhang, Q. (eds) Modeling, Stochastic Control, Optimization, and Applications. The IMA Volumes in Mathematics and its Applications, vol 164. Springer, Cham. https://doi.org/10.1007/978-3-030-25498-8_17
Download citation
DOI: https://doi.org/10.1007/978-3-030-25498-8_17
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-25497-1
Online ISBN: 978-3-030-25498-8
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)