Multi-Period Mean-Variance Portfolio Selection with State-Dependent Exit Probability and Bankruptcy State
- 1 Department of Mathematics, Curtin University, Perth, Australia
- 2 Department of Mathematics, Curtin University, Perth, Australia
- 3 Department of Mathematics, Curtin University, Perth, Australia
Abstract
Based on the mean-variance portfolio selection under multi-period criterion, this paper focuses on the study of the uncertain time horizon and the regime-switching market including the bankruptcy state, where the conditional distribution of exit time is followed by the market state. When the market enters the bankruptcy state, investors are assumed to get back δ part of the wealth from the bankrupt company, where δ refers to the retrieval rate. By introducing the Lagrange multiplier λ , we create an innovative expression for the wealth process and the iterative representation of the value function to obtain the analytical expression of the optimal strategy and the corresponding efficient frontier. Besides, some special cases and numerical examples are presented to demonstrate the effects of state-dependent exit probability and bankruptcy state on the investment strategy.
- Markowitz, H. (1952) Portfolio Selection. The Journal of Finance, 7, 77-91. https://doi.org/10.1111/j.1540-6261.1952.tb01525.x
- Merton, R.C. (1972) An Analytic Derivation of the Efficient Portfolio Frontier. Journal of Financial and Quantitative Analysis, 7, 1851-1872. https://doi.org/10.2307/2329621
- Li, D. and Ng, W.-L. (2000) Optimal Dynamic Portfolio Selection: Multiperiod Mean-Variance Formulation. Mathematical Finance, 10, 387-406. https://doi.org/10.1111/1467-9965.00100
- Zhou, X.Y. and Li, D. (2000) Continuous-Time Mean-Variance Portfolio Selection: A Stochastic lq Framework. Applied Mathematics and Optimization, 42, 19-33. https://doi.org/10.1007/s002450010003
- Neftçi, S.N. (1984) Are Economic Time Series Asymmetric over the Business Cycle? Journal of Political Economy, 92, 307-328. https://doi.org/10.1086/261226
- Zhou, X. and Yin, G. (2003) Markowitz’s Mean-Variance Portfolio Selection with Regime Switching: A Continuous-Time Model. SIAM Journal on Control and Optimization, 42, 1466-1482. https://doi.org/10.1137/S0363012902405583
- Yin, G. and Zhou, X.Y. (2004) Markowitz’s Mean-Variance Portfolio Selection with Regime Switching: From Discrete-Time Models to Their Continuous-Time Limits. IEEE Transactions on Automatic Control, 49, 349-360. https://doi.org/10.1109/TAC.2004.824479
- Çakmak, U. and Özekici, S. (2006) Portfolio Optimization in Stochastic Markets. Mathematical Methods of Operations Research, 63, 151-168. https://doi.org/10.1007/s00186-005-0020-x
- Xie, S. (2009) Continuous-Time Mean-Variance Portfolio Selection WITH Liability and Regime Switching. Insurance: Mathematics and Economics, 45, 148-155. https://doi.org/10.1016/j.insmatheco.2009.05.005
- Elliott, R.J. and Siu, T.K. (2010) On Risk Minimizing Portfolios under a Markovian Regime Switching Black-Scholes Economy. Annals of Operations Research, 176, 271-291. https://doi.org/10.1007/s10479-008-0448-5
- Guo, W.J. and Hu, Q.Y. (2005) Multi-Period Portfolio Optimization When Exit Time Is Uncertain. Journal of Management Sciences in China, 8, 14-19.
- Yi, L., Li, Z. and Li, D. (2008) Multi-Period Portfolio Selection for Asset-Liability Management with Uncertain Investment Horizon. Journal of Industrial & Management Optimization, 4, 535-552. https://doi.org/10.3934/jimo.2008.4.535
- Wu, H. and Li, Z. (2011) Multi-Period Mean-Variance Portfolio Selection with Markov Regime Switching and Uncertain Time-Horizon. Journal of Systems Science and Complexity, 24, 140-155. https://doi.org/10.1007/s11424-011-9184-z