Recursive risk measures under regime switching applied to portfolio selection

References

• Abramowitz, M. and Stegun, I.A., Handbook of Mathematical Functions with Formulas, Graphs and Mathematical Tables, 1971 (Dover: New York).
   Google Scholar
• Alizadeh, F. and Goldfarb, D., Second-order cone programming. Math. Program. Ser. B, 2005, 95, 3–51.
   Web of Science ®Google Scholar
• Andreev, A. and Kanto, A., CVAR estimation using non-integer values of degrees of freedom in Student’s t-distribution. J. Risk, 2005, 7, 55–61.
   Google Scholar
• Ang, A. and Bekaert, G., International asset allocation with regime shifts. Rev. Financ. Stud., 2002, 15, 1137–1187.
   Web of Science ®Google Scholar
• Artzner, P., Delbaen, F., Eber, J.M., Heath, D. and Ku, H., Coherent multiperiod risk adjusted values and Bellmans principle. Ann. Oper. Res., 2007, 152, 5–22.
   Web of Science ®Google Scholar
• Çakmak, U. and Özekici, S., Portfolio optimization in stochastic markets. Math. Meth. Oper. Res., 2006, 63, 151–168.
   Web of Science ®Google Scholar
• Chen, Z., Li, G. and Guo, J., Optimal investment policy in the time consistent mean-variance formulation. Insur. Math. Econ., 2013, 52, 145–156.
   Web of Science ®Google Scholar
• Chen, Z., Liu, J., Li, G. and Yan, Z., Composite time-consistent multi-period risk measure and its application in optimal portfolio selection. TOP, 2016, 24, 515–540.
   Web of Science ®Google Scholar
• Chen, N.F., Roll, R. and Ross, S., Economic forces and the stock market. J. Bus., 1986, 59, 383–403.
   Web of Science ®Google Scholar
• Cheridito, P., Delbaen, F. and Kupper, M., Dynamic monetary risk measures for bounded discrete-time processes. Electron. J. Probab., 2006, 11, 57–106.
   Web of Science ®Google Scholar
• Claro, J. and de Sousa, J.P., A multiobjective metaheuristic for a mean-risk multistage capacity investment problem with process flexibility. Comput. Oper. Res., 2012, 39, 838–849.
   Web of Science ®Google Scholar
• Cox, D., Statistical analysis of time series: Some recent developments. Scand. J. Stat., 1981, 8, 93–115.
   Web of Science ®Google Scholar
• Cui, X.Y., Li, D., Wang, S.Y. and Zhu, S.S., Better than dynamic mean-variance: Time inconsistency and free cash flow stream. Math. Financ., 2012, 22, 346–378.
   Web of Science ®Google Scholar
• Czichowsky, C., Time-consistent mean-variance portfolio selection in discrete and continuous time. Financ. Stoch., 2013, 17, 227–271.
   Web of Science ®Google Scholar
• Detlefsen, K. and Scandolo, G., Conditional and dynamic convex risk measures. Financ. Stoch., 2005, 9, 539–561.
   Web of Science ®Google Scholar
• Dumas, B. and Luciano, E., An exact solution to a dynamic portfolio choice problem under transactions costs. J. Financ., 1991, 46, 577–595.
   Web of Science ®Google Scholar
• Elton, E.J. and Gruber, M.J., On the optimality of some multiperiod portfolio selection criteria. J. Bus., 1974, 47, 231–243.
   Web of Science ®Google Scholar
• Elton, E., Gruber, M., Brown, S. and Goetzmann, W., Modern Portfolio Theory and Investment Analysis, 7th ed., 2007 (Wiley: New York).
   Google Scholar
• Fábián, C.I., Handling CVaR objectives and constraints in two-stage stochastic models. Eur. J. Oper. Res., 2008, 191, 888–911.
   Web of Science ®Google Scholar
• Fama, E.F. and French, K.R., Common risk factors in the returns on stocks and bonds. J. Financ. Econ., 1993, 33, 3–56.
   Web of Science ®Google Scholar
• Faug, K., Kotz, S. and Ng, K.W., Symmetric Multivariate and Related Distributions, 1990 (Chapman and Hall: London).
   Google Scholar
• Föllmer, H. and Penner, I., Convex risk measures and the dynamics of their penalty functions. Stat. Decis., 2006, 24, 61–96.
   Google Scholar
• Guidolin, M. and Timmermann, A., International asset allocation under regime switching, skew and kurtosis preference. Rev. Financ. Stud., 2008, 21, 889–935.
   Web of Science ®Google Scholar
• Güpınara, N. and Rustem, B., Worst-case robust decisions for multi-period mean-variance portfolio optimization. Eur. J. Oper. Res., 2007, 127, 981–1000.
   Google Scholar
• Hamilton, J.D., Analysis of time series subject to changes in regime. J. Econom., 1990, 45, 39–70.
   Web of Science ®Google Scholar
• Heikkinen, V.P. and Kanto, A., Value-at-risk estimation using non-integer degrees of freedom of student’s distribution. J. Risk, 2002, 4, 77–84.
   Google Scholar
• Honda, T., Optimal portfolio choice for unobservable and regime-switching mean returns. J. Econ. Dyn. Control, 2003, 28, 45–78.
   Web of Science ®Google Scholar
• Kovacevic, R., Conditional risk and acceptability mappings as Banach-Lattice valued mappings. Stat. Risk Model., 2012, 29, 1–18.
   Google Scholar
• Li, D. and Ng, W.L., Optimal dynamic portfolio selection, multiperiod mean-variance formulation. Math. Financ., 2000, 10, 387–406.
   Web of Science ®Google Scholar
• Liu, J. and Chen, Z.P., Regime-dependent robust risk measures with application in portfolio selection. Procedia Comput. Sci., 2014, 31, 344–350.
   Google Scholar
• Ma, Y., Xu, K., MacLean, L. and Zhao, Y.G., A portfolio optimization model with regime-switching risk factors for sector exchange traded funds. Pac. J. Optim., 2011, 7, 455–470.
   Web of Science ®Google Scholar
• Mulvey, J.M. and Zhao, Y.G., An investment model via regime-switching economic indicators. Working Paper, Princeton University, 2010.
   Google Scholar
• Pflug, G.Ch. and Pichler, A., Time-inconsistent multistage stochastic programs: Martingale bounds. Eur. J. Oper. Res., 2016, 249, 155–163.
   Web of Science ®Google Scholar
• Pflug, G.Ch. and Römisch, W., Modeling, Measuring and Managing Risk, 2007 (World Scientific: Singapore).
   Google Scholar
• Rockafellar, R. and Uryasev, S., Conditional value-at-risk for general loss distributions. J. Bank. Financ., 2002, 26, 1443–1471.
   Web of Science ®Google Scholar
• Roorda, B., Schumacher, J.M. and Engwerda, J.C., Coherent acceptability measures in multiperiod models. Math. Financ., 2005, 15, 589–612.
   Web of Science ®Google Scholar
• Ruszczyński, A., Risk-averse dynamic programming for Markov decision processes. Math. Program. Ser. B, 2010, 125, 235–261.
   Web of Science ®Google Scholar
• Ruszczyński, A. and Shapiro, A., Conditional risk mappings. Math. Oper. Res., 2006, 31, 544–561.
   Web of Science ®Google Scholar
• Shapiro, A., Dentcheva, D. and Ruszczyński, A., Lectures on Stochastic Programming: Modeling and Theory, 2009 (SIAM: Philadelphia, PA).
   Google Scholar
• Sharpe, W.F., Capital asset prices: A theory of market equilibrium under conditions of risk. J. Financ., 1964, 19, 425–442.
   Web of Science ®Google Scholar
• Topaloglou, N., Vladimirou, H. and Zenios, S.A., A dynamic stochastic programming model for international portfolio management. Eur. J. Oper. Res., 2008, 185, 1501–1524.
   Web of Science ®Google Scholar
• Wang, T., A class of dynamic risk measure. Working Paper, University of British Columbia, 1999.
   Google Scholar
• Weber, S., Distribution-invariant risk measures, information, and dynamic consistency. Math. Financ., 2006, 16, 419–441.
   Web of Science ®Google Scholar
• Wu, H. and Li, Z., Multi-period mean-variance portfolio selection with regime switching and a stochastic cash flow. Insur. Math. Econ., 2012, 50, 371–384.
   Web of Science ®Google Scholar