Optimal asset allocation with stochastic interest rates in regime-switching models. (English) Zbl 1396.91708
Summary: This paper focuses on optimal asset allocation with stochastic interest rates in regime-switching models. A class of stochastic optimal control problems with Markovian regime-switching is formulated for which a verification theorem is provided. The theory is applied to solve two portfolio optimization problems (a portfolio of stock and savings account and a portfolio of mixed stock, bond and savings account) while a regime-switching Vasicek model is assumed for the interest rate. Closed-form solutions are obtained for a regime-switching power utility function. Numerical results are provided to illustrate the impact of regime-switching on the optimal investment decisions.
MSC:
| 91G10 | Portfolio theory |
| 91G30 | Interest rates, asset pricing, etc. (stochastic models) |
| 93E20 | Optimal stochastic control |
Keywords:
optimal asset allocation; portfolio optimization; stochastic control; regime-switching models; stochastic interest rate; power utilityReferences:
| [1] | Bansal, R.; Zhou, H., Term structure of interest rates with regime shifts, Journal of Finance, 57, 1997-2043, (2002) |
| [2] | Bäuerle, N.; Rieder, U., Portfolio optimization with Markov-modulated stock prices and interest rates, IEEE Transactions on Automatic Control, 49, 3, 442-447, (2004) · Zbl 1366.91135 |
| [3] | Bäuerle, N.; Rieder, U., Portfolio optimization with jumps and unobservable intensity process, Mathematical Finance, 17, 2, 205-224, (2007) · Zbl 1186.91189 |
| [4] | Fleming, W. H.; Soner, H. M., Controlled Markov Processes and Viscosity Solutions, 25, (2006), Springer-Verlag, New York · Zbl 1105.60005 |
| [5] | Fu, J.; Wei, J.; Yang, H., Portfolio optimization in a regime-switching market with derivatives, European Journal of Operational Research, 233, 184-192, (2014) · Zbl 1339.91108 |
| [6] | Hardy, M., A regime-switching model for long-term stock returns, North American Actuarial Journal, 5, 41-53, (2001) · Zbl 1083.62530 |
| [7] | Korn, R.; Kraft, H., A stochastic control approach to portfolio problems with stochastic interest rates, SIAM Journal on Control and Optimization, 40, 4, 1250-1269, (2001) · Zbl 1020.93029 |
| [8] | Protter, P., Stochastic Integration and Differential Equations, (2005), Springer-Verlag, Berlin Heidelberg |
| [9] | Rieder, U.; Bäuerle, N., Portfolio optimization with unobservable Markov-modulated drift process, Journal of Applied Probability, 42, 2, 362-378, (2005) · Zbl 1138.93428 |
| [10] | Sass, J.; Haussmann, U., Optimizing the terminal wealth under partial information: the drift process as a continuous time Markov chain, Finance and Stochastics, 8, 553-577, (2004) · Zbl 1063.91040 |
| [11] | Sotomayor, L.; Cadenillas, A., Explicit solutions of consumption-investment problems in financial markets with regime switching, Mathematical Finance, 19, 2, 251-279, (2009) · Zbl 1168.91400 |
| [12] | Yin, G.; Zhang, Q., Continuous-Time Markov Chains and Applications: A Singular Perturbation Approach, (1998), Springer-Verlag, New York · Zbl 0896.60039 |
| [13] | Yin, G.; Zhu, C., Hybrid Switching Diffusions, (2010), Springer-Verlag, New York · Zbl 1279.60007 |
| [14] | Zhang, X.; Siu, T.; Meng, Q., Portfolio selection in the enlarged Markovian regime-switching market, SIAM Journal on Control and Optimization, 48, 5, 3368-3388, (2010) · Zbl 1202.91308 |
| [15] | Zhang, Q.; Yin, G., Nearly-optimal asset allocation in hybrid stock investment models, Journal of Optimization Theory and Applications, 121, 2, 419-449, (2004) · Zbl 1090.91049 |
| [16] | Zhou, X.; Yin, G., Markowitz’s mean-variance portfolio selection with regime switching: A continuous-time model, SIAM Journal on Control and Optimization, 42, 1466-1482, (2003) · Zbl 1175.91169 |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
