Free Access
Volume 25, 2019
Article Number 64
Number of page(s) 60
Published online 25 October 2019
  1. T. Björk, M. Khapko and A. Murgoci, On time-inconsistent stochastic control in continuous time. Financ. Stoch. 21 (2017) 331–360. [CrossRef] [Google Scholar]
  2. T. Björk and A. Murgoci, A theory of Markovian time-inconsistent stochastic control in discrete time. Financ. Stoch. 18 (2014) 545–592. [CrossRef] [Google Scholar]
  3. T. Björk, A. Murgoci and X.Y. Zhou, Mean-variance portfolio optimization with state-dependent risk aversion. Math. Financ. 24 (2014) 1–24. [Google Scholar]
  4. S.N. Cohen and R.J. Elliott, Solutions of backward stochastic differential equations on Markov chains. Commun. Stoch. Anal. 2 (2008) 251–262. [Google Scholar]
  5. C. Donnelly, Sufficient stochastic maximum principle in a regime-switching diffusion model. Appl. Math. Optim. 64 (2011) 155–169. [Google Scholar]
  6. C. Donnelly and A.J. Heunis, Quadratic risk minimuzation in a regime-swtching model with portfolio constraints. SIAM J. Control Optim. 50 (2012) 2431–2461. [CrossRef] [Google Scholar]
  7. D. Duffie and L.G. Epstein, Stochastic differential utility. Econometrica 60 (1992) 353–394. [Google Scholar]
  8. D. Duffie and L.G. Epstein, Asset pricing with stochastic differential utility. Rev. Financ. Stud. 5 (1992) 411–436. [Google Scholar]
  9. D. Duffie and P.L. Lions, PDE solutions of stochastic differential utility. J. Math. Econom. 21 (1992) 577–606. [CrossRef] [Google Scholar]
  10. S.D. Eidel’man, Parabolic Systems. North Holland Publishing Company, Amsterdam (1969). [Google Scholar]
  11. I. Ekeland and A. Lazrak, The golden rule when preferences are time inconsistent. Math. Financ. Econ. 4 (2010) 29–55. [CrossRef] [Google Scholar]
  12. N. El Karoui, S. Peng and M.C. Quenez, Backward stochastic differential equations in finance. Math. Financ. 7 (1997) 1–71. [Google Scholar]
  13. N.C. Framstad, B.K. ∅ksendal and A. Sulem, Sufficient stochastic maximum principle for the optimal control of jump diffusions and applications to finance. J. Optim. Theory Appl. 121 (2004) 77–98. [Google Scholar]
  14. A. Friedman, Partial Differential Equations of Parabolic Type. Prentice Hall, Inc., Englewood Cliffs, NJ (1964). [Google Scholar]
  15. J.D. Hamilton, A new approach to the economic analysis of nonstationry time series and the business cycle. Econometrica 57 (1989) 357–384. [Google Scholar]
  16. A.J. Heunis, Utility maximization in a regime switching model wih convex portfolio constratints and margin requirements: optimality relations and explicit solutions. SIAM J. Control Optim. 53 (2015) 2608–2656. [CrossRef] [Google Scholar]
  17. Y. Hu, H. Jin and X.Y. Zhou, Time-inconsistent stochastic linear-quadratic control. SIAM J. Control Optim. 50 (2012) 1548–1572. [CrossRef] [Google Scholar]
  18. D. Hume, A Treatise of Human Nature, 1st edn. (1739); Reprint. Oxford University Press, New York (1978). [Google Scholar]
  19. C. Karnam, J. Ma and J. Zhang, Dynamic approaches for some time inconsistent problems. Preprint arXiv:1604.03913[math.OC] (2016). [Google Scholar]
  20. H. Kraft and F.T. Seifried, Stochastic differential utility as the continuous-time limit of recursive utility. J. Econ. Theory 151 (2014) 528–550. [Google Scholar]
  21. T. Kruse and A. Popier, BSDEs with monotone generator driven by Brownian and Poisson noises in a general filtration. Stochastics 88 (2016) 491–539. [MathSciNet] [Google Scholar]
  22. T. Kruse and A. Popier, Lp-solution for BSDEs with jumps in the case p < 2: Corrections to the paper BSDEs with monotone generator driven by Brownian and Poisson noises in a general filtration. Stochastics 89 (2017) 1201–1227 [CrossRef] [Google Scholar]
  23. D. Laibson, Golden eggs and hyperbolic discounting. Quart. J. Econ. 112 (1997) 443–477. [CrossRef] [Google Scholar]
  24. A. Lazrak, Generalized stochastic differential utility and preference for information. Ann. Appl. Probab. 14 (2004) 2149–2175. [Google Scholar]
  25. A. Lazrak and M.C. Quenez, A generalized stochastic differential utility. Math. Oper. Res. 28 (2003) 154–180. [CrossRef] [Google Scholar]
  26. J. Ma, P. Protter and J. Yong, Solving forward-backward stochastic differential equations explicitly – a four step scheme. Probab. Theory Relat. Fields 98 (1994) 339–359. [Google Scholar]
  27. J. Ma, Z. Wu, D. Zhang and J. Zhang, On well-posedness of forward-backward SDEs – a unified approach. Ann. Appl. Probab. 25 (2015) 2168–2214. [Google Scholar]
  28. J. Ma and J. Yong, Forward-Backward Stochastic Differential Equations and Their Applications. Vol. 1702 of Lecture Notes in Mathematics. Springer-Verlag, Berlin (1999). [Google Scholar]
  29. J. Marin-Solano and J. Navas, Consumption and portfolio rules for time-inconsistent investors. Eur. J. Oper. Res. 201 (2010) 860–872. [Google Scholar]
  30. J. Marin-Solano and E.V. Shevkoplyas, Non-constant discounting and differential games with random time horizon. Automatica 47 (2011) 2626–2638. [CrossRef] [Google Scholar]
  31. B.K. ∅ksendal and A. Sulem, Applied Stochastic Control of Jump Diffusions. Springer-Verlag, Berlin (2005). [Google Scholar]
  32. I. Palacios-Huerta, Time-inconsistent preferences in Adam Smith and David Hume. Hist. Political Econ. 35 (2003) 241–268. [CrossRef] [Google Scholar]
  33. E. Pardoux and S. Peng, Adapted solution of backward stochastic equation. Syst. Control Lett. 14 (1990) 55–61. [Google Scholar]
  34. R.A. Pollak, Consistent planning. Rev. Econ. Stud. 35 (1968) 185–199. [Google Scholar]
  35. R. Situ, Theory of Stochastic Differential Equations with Jumps and Applications: Mathematical and Analytical Techniques with Applications to Engineering. Springer Science & Business Media, New York (2006). [Google Scholar]
  36. A. Smith, The Theory of Moral Sentiments, 1st edn. (1759). Reprint, Oxford University Press, New York (1976). [Google Scholar]
  37. L.R. Sotomayor and A. Cadenilla, Explicit solutions of consumption-investment problems in financecial markets with regime switching. Math. Financ. 19 (2009) 251–279. [Google Scholar]
  38. R.H. Strotz, Myopia and inconsistency in dynamic utility maximization. Rev. Econ. Stud. 23 (1955) 165–180. [Google Scholar]
  39. J. Wei, Time-inconsistent optimal control problems with regime-switching. Math. Control Relat. Fields 7 (2017) 585–622. [CrossRef] [Google Scholar]
  40. Q. Wei, J. Yong and Z. Yu, Time-inconsistent recrusive stochastic optimal control problems. SIAM J. Control Optim. 55 (2017) 4156–4201. [CrossRef] [Google Scholar]
  41. G. Yin and C. Zhu, Hybrid Switching Diffusions: Properties and Applications, Vol. 63. Springer Science & Business Media, New York (2009). [Google Scholar]
  42. J. Yong, Time-inconsistent optimal control problems and the equilibrium HJB equation. Math. Control Relat. Fields 2 (2012) 271–329. [CrossRef] [Google Scholar]
  43. J. Yong, Time-inconsistent optimal control problems, in Proceedings of the International Congress of Mathematicians (2014) 947–969. [Google Scholar]
  44. J. Yong, Linear-quadratic optimal control problems for mean-field stochastic differential equations – time-consistent solutions. Trans. AMS 369 (2017) 5467–5523. [CrossRef] [Google Scholar]
  45. J. Yongand X.Y. Zhou, Stochastic Control: Hamiltonian Systems and HJB Equations. Springer-Verlag, New York (1999). [Google Scholar]
  46. J. Zhang, Backward Stochastic Differential Equations – From Linear to Fully Nonlinear Theory. Springer, New York (2017). [CrossRef] [Google Scholar]
  47. X. Zhang, R.J. Elliott and T.K. Siu, A stochastic maximum principle for a Markov regime-swtching jump-diffusion model and its application to finance. SIAM J. Control Optim. 50 (2012) 964–990. [CrossRef] [Google Scholar]
  48. X.Y. Zhou and G. Yin, Markowitz’s mean-varaince portfolio selection with regime swtching: a contionus-time model. SIAM J. Control Optim. 42 (2003) 1466–1482. [CrossRef] [Google Scholar]

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