Time Consistency of the Mean-Risk Problem

Published Online:https://doi.org/10.1287/opre.2020.2002

References

  • Ankirchner S , Dermoune A (2011) Multiperiod mean-variance portfolio optimization via market cloning. Appl. Math. Optim. 64(1):135–154.CrossrefGoogle Scholar
  • Bäuerle N , Mundt A (2008) Dynamic mean-risk optimization in a binomial model. Math. Methods Oper. Res. 70(2):219–239.CrossrefGoogle Scholar
  • Bellman R (1954) The theory of dynamic programming. Bull. Amer. Math. Soc. (N.S.) 60(6):503–515.CrossrefGoogle Scholar
  • Bertsekas DP (2005) Dynamic Programming and Optimal Control (Athena Scientific, Belmont, MA).Google Scholar
  • Björk T , Murgoci A (2014) A theory of Markovian time-inconsistent stochastic control in discrete time. Finance Stochastics 18(3):545–592.CrossrefGoogle Scholar
  • Björk T , Murgoci A , Yu Zhou X (2014) Mean variance portfolio optimization with state dependent risk aversion. Math. Finance 24(1):1–24.CrossrefGoogle Scholar
  • Brown TA , Strauch RE (1965) Dynamic programming in multiplicative lattices. J. Math. Anal. Appl. 12(2):364–370.CrossrefGoogle Scholar
  • Cheridito P , Stadje M (2009) Time-inconsistency of var and time-consistent alternatives. Finance Res. Lett. 6(1):40–46.CrossrefGoogle Scholar
  • Ciripoi D , Löhne A , Weißing B (2018) A vector linear programming approach for certain global optimization problems. J. Global Optim. 72(2):347–372.CrossrefGoogle Scholar
  • Cui X , Li D , Wang S , Zhu S (2012) Better than dynamic mean-variance: Time inconsistency and free cash flow stream. Math. Finance 22(2):346–378.CrossrefGoogle Scholar
  • Detlefsen K , Scandolo G (2005) Conditional and dynamic convex risk measures. Finance Stochastics 9(4):539–561.CrossrefGoogle Scholar
  • Eichhorn A , Römisch W (2005) Polyhedral risk measures in stochastic programming. SIAM J. Optim. 16(1):69–95.CrossrefGoogle Scholar
  • Feinstein Z , Rudloff B (2017) A recursive algorithm for multivariate risk measures and a set-valued Bellman’s principle. J. Global Optim. 68(1):47–69.CrossrefGoogle Scholar
  • Hamel AH , Löhne A , Rudloff B (2014) Benson type algorithms for linear vector optimization and applications. J. Global Optim. 59(4):811–836.CrossrefGoogle Scholar
  • Hamel AH , Heyde F , Löhne A , Rudloff B , Schrage C (2015) Set optimization—a rather short introduction. Hamel AH, Heyde F, Löhne A, Rudloff B, Schrage C, eds. Set Optimization and Applications - The State of the Art (Springer, Berlin), 65–141.Google Scholar
  • Karnam C , Ma J , Zhang J (2017) Dynamic approaches for some time inconsistent optimization problems. Ann. Appl. Probab. 27(6):3435–3477.CrossrefGoogle Scholar
  • Korn R , Müller S (2009) The decoupling approach to binomial pricing of multi-asset options. J. Comput. Finance 12(3):1–30.CrossrefGoogle Scholar
  • Li D (1990) Multiple objectives and non-separability in stochastic dynamic programming. Internat. J. Systems Sci. 21(5):933–950.CrossrefGoogle Scholar
  • Li D , Haimes YY (1987) The envelope approach for multiobjective optimization problems. IEEE Trans. Systems Man Cybernetics 17(6):1026–1038.CrossrefGoogle Scholar
  • Li D , Haimes YY (1990) New approach for nonseparable dynamic programming problems. J. Optim. Theory Appl. 64(2):311–330.CrossrefGoogle Scholar
  • Li D , Ng WL (2000) Optimal dynamic portfolio selection: Multiperiod mean-variance formulation. Math. Finance 10(3):387–406.CrossrefGoogle Scholar
  • Löhne A (2011) Vector Optimization with Infimum and Supremum (Springer, Berlin).CrossrefGoogle Scholar
  • Löhne A , Weißing B (2016) Equivalence between polyhedral projection, multiple objective linear programming and vector linear programming. Math. Methods Oper. Res. 84(2):411–426.CrossrefGoogle Scholar
  • Löhne A , Rudloff B , Ulus F (2014) Primal and dual approximation algorithms for convex vector optimization problems. J. Global Optim. 60(4):713–736.CrossrefGoogle Scholar
  • Mossin J (1968) Optimal multiperiod portfolio policies. J. Bus. 41(2):215–229.CrossrefGoogle Scholar
  • Riedel F (2004) Dynamic coherent risk measures. Stochastic Processes Their Appl. 112(2):185–200.CrossrefGoogle Scholar
  • Rudloff B , Street A , Valladão DM (2014) Time consistency and risk averse dynamic decision models: Definition, interpretation and practical consequences. Eur. J. Oper. Res. 234(3):743–750.CrossrefGoogle Scholar
  • Rudloff B , Ulus F , Vanderbei R (2017) A parametric simplex algorithm for linear vector optimization problems. Math. Program. 163(1):213–242.CrossrefGoogle Scholar
  • Ruszczyński A , Vanderbei R (2003) Frontiers of stochastically nondominated portfolios. Econometrica 71(4):1287–1297.CrossrefGoogle Scholar
INFORMS site uses cookies to store information on your computer. Some are essential to make our site work; Others help us improve the user experience. By using this site, you consent to the placement of these cookies. Please read our Privacy Statement to learn more.