在行为金融前景理论框架下研究跨市场间的状态转移资产配置问题，构建隐Markov——混合正态分布模型描述股票、债券和商品混合市场间的状态特征，用Baum-Welch算法估计模型参数，并利用状态转移思想进行情景生成建立多阶段随机优化模型。进一步，以我国股票、债券和商品混合市场的实际数据为背景，利用滚动窗口方法实证分析基于状态转移的多阶段随机模型的表现，并与忽略状态转移特征的基准模型、等权重组合、沪深300指数的结果进行对比。结果表明，与其他组合相比，基于状态转移的投资组合有助于规避风险，且混合市场间的状态转移信息能够对前景理论投资者的最优投资决策产生影响。
With the increasing interactivity of financial markets, the single risk market cannot meet the actual investment needs. There have been academic studies indicating that the fluctuation of asset returns in the market can be influenced by the economic cycle which shows different characteristics under different market conditions. Meanwhile, in the actual investment, investors often deviate from the expected utility theory. In this paper, under the framework of prospect theory and behavioral finance, an asset allocation problem among cross-markets with regime switching is studied. Hidden Markov regime switching-mixture normal distribution is constructed to describe time-varying regimes in the stock market, the bond market and the commodity market, the parameters of which are estimated by the Baum-Welch algorithm. Moreover, with scenarios generated under regime switching, a multi-period stochastic optimized model is constructed. Further, against the background of the stock market, the bond market and the commodity market in China, the performance of multi-period stochastic model is empirically analyzed by the use of rolling window method, which is compared with the results of standard dynamic model ignoring regime switching, equally weighted portfolio and hs300 index. It is concluded that compared with other portfolio, regime switching portfolio helps avoid risk, and under the prospect theory, regime switching information of hybrid markets can have an effect on optimal decision of prospect theory investors. The conclusions show that compared with risk investment with single market, the multi-period asset allocation of cross-markets under the framework of the prospect theory contributes to avoiding risk. Especially when the market performs poorly, introducing regime switching information can affect the investment decision, and is beneficial for investors to obtain stable returns. Above all, certain reference meanings can be provided for the risk management of capital market in China and institutional investors and fund managers may be helped hold diversified portfolio.
[1] Guidolin M, Timmermann A. Economic implications of bull and bear regimes in UK stock and bond returns[J]. The Economic Journal, 2005, 115(500):111-143.
[2] Hamilton J D. A new approach to the economic analysis of nonstationary time series and the business cycle[J]. Econometrica, 1989, 57(2):357-384.
[3] 蔡伟宏, 唐齐鸣. 基于无穷状态转换模型的中国股票市场收益率分析[J]. 中国管理科学, 2014, 22(1):10-19.
[4] Levy M, Kaplanski G. Portfolio selection in a two-regime world[J]. European Journal of Operational Research, 2015,242(2):514-524.
[5] Dou P Y, Gallagher D R, Schneider D, et al. Cross-region and cross-sector asset allocation with regimes[J]. Accounting and Finance, 2014, 54(3):809-846.
[6] Luo Pengfei, Yang Zhaojun. Real options and contingent convertibles with regime switching[J]. Journal of Economic Dynamics and Control, 2017, 75:122-135.
[7] Reus L, Mulvey J M. Dynamic allocations for currency futures under switching regimes signals[J]. European Journal of Operational Research, 2016, 253(1):85-93.
[8] Salhi K, Deaconu M, Lejay A, et al. Regime switching model for financial data:Empirical risk analysis[J]. Physica A:Statistical Mechanics and Its Applications, 2016, 461:148-157.
[9] Zhu Dongmei, Lu Jiejun, Ching W K, et al. Discrete-time optimal asset allocation under Higher-Order Hidden Markov Model[J]. Economic Modelling, 2017, 66:223-232.
[10] Liu Zhenya, Wang Shixuan. Decoding Chinese stock market returns:Three-state hidden semi-Markov model[J]. Pacific-Basin Finance Journal, 2017, 44:127-149.
[11] Hou Chenghan. Infinite hidden Markov switching VARs with application to macroeconomic forecast[J]. International Journal of Forecasting, 2017, 33(4):1025-1043.
[12] 李仲飞, 姚海洋. 不确定退出时间和随机市场环境下风险资产的动态投资组合选择[J]. 系统工程理论与实践, 2014, 34(11):2737-2747.
[13] 周艳丽, 吴洋, 葛翔宇. 一类高新技术企业专利权价值的实物期权评估方法——基于跳扩散过程和随机波动率的美式期权的建模与模拟[J]. 中国管理科学, 2016, 24(6):19-28.
[14] Bae G I, Kim W C, Mulvey J M. Dynamic asset allocation for varied financial markets under regime switching framework[J]. European Journal of Operational Research, 2014,234(2):50-458.
[15] Zhang Miao, Chen Ping. Mean-variance portfolio selection with regime switching under shorting prohibition[J]. Operations Research Letters, 2016, 44(5):658-662.
[16] Siegel J,Thaler R H. Anomalies:The equity premium puzzle[J].Journal of Economic Perspectives, 1997, 11(1):191-200.
[17] Kahneman D, Tversky A. Prospect theory:An analysis of decision under risk[J]. Econometrica, 1979, 47(2):263-291.
[18] Guan Guohui, Liang Zongxia. Optimal management of DC pension plan under loss aversion and Value-at-Risk constraints[J]. Insurance Mathematics and Economics, 2016, 69:224-237.
[19] 王佳, 金秀, 苑莹, 等. 基于损失厌恶和模糊厌恶的分布鲁棒投资组合模型[J].系统工程理论与实践, 2016, 36(2):288-296.
[20] Easley D, Yang Liyan. Loss aversion, survival and asset prices[J]. Journal of Economic Theory, 2015, 160:494-516.
[21] Fulga C. Portfolio optimization under loss aversion[J]. European Journal of Operational Research, 2016,251(1):310-322.
[22] Guidolin M, Timmermann A. Asset allocation under multivariate regime switching[J]. Journal of Economic Dynamic and Control, 2007, 31(11):3503-3544.
[23] Fraser A M. Hidden Markov Models and dynamical systems[M]. Philadelphia, USA:Society for Industrial and Applied Mathematics, 2008.
[24] Mitra S, Date P. Regime switching volatility calibration by the Baum-Welch method[J]. Journal of Computational and Applied Mathematics, 2010, 234(12):3243-3260.
[25] Best M J, Grauer R R, Hlouskova J, et al. Loss aversion with kinked linear utility functions[J]. Computational Economics, 2014,44(1):45-65.
