Optimal Learning Under Robustness and Time-Consistency

Published Online:https://doi.org/10.1287/opre.2019.1899

References

  • Arrow KJ, Hurwicz L (1972) An optimality criterion for decision making under ignorance. Carter C, Ford J, eds. Uncertainty and Expectations in Economics (Basil Blackwell, Oxford, UK), 1–11.Google Scholar
  • Arrow KJ, Blackwell D, Girshick MA (1949) Bayes and minimax solutions of sequential decision problems. Econometrica 17(3/4):214–244.CrossrefGoogle Scholar
  • Berger JO (1984) The robust Bayesian viewpoint. Kadane J, ed. Robustness in Bayesian Statistics (North Holland, Amsterdam), 63–124.Google Scholar
  • Berger JO (1985) Statistical Decision Theory and Bayesian Analysis (Springer, New York).CrossrefGoogle Scholar
  • Berger JO (1994) An overview of robust Bayesian analysis (with discussion). TEST 3(1):5–124.CrossrefGoogle Scholar
  • Borodin A, Salminen P (2015) Handbook of Brownian Motion—Facts and Formulae, 2nd ed. (Birkhauser, Basel, Switzerland).Google Scholar
  • Caro F, Das Gupta A (2015) Robust control of the multi-armed bandit problem. Ann. Oper., ePub ahead of print August 21, https://doi.org/10.1007/s10479-015-1965-7.CrossrefGoogle Scholar
  • Chen Z, Epstein LG (2002) Ambiguity, risk and asset returns in continuous time. Econometrica 70(4):1403–1443.CrossrefGoogle Scholar
  • Cheng X, Riedel F (2013) Optimal stopping under ambiguity in continuous time. Math. Financial Econom. 7(1):29–68.CrossrefGoogle Scholar
  • Choi H (2016) Learning under ambiguity: Portfolio choice and asset returns. Working paper, City University of Hong Kong, Kowloon Tong, Hong Kong.Google Scholar
  • Ebert S, Strack P (2018) Never, ever getting started: On prospect theory without commitment Working paper, Frankfurt School of Finance and Management, Frankfurt, Germany.Google Scholar
  • El Karoui N, Kapoundijian C, Pardoux E, Peng S, Quenez M (1997) Reflected solutions of backward SDE’s and related obstacle problems for PDE’s. Ann. Probab. 25(2):702–737.CrossrefGoogle Scholar
  • Ellsberg D (1961) Risk, ambiguity, and the Savage axioms. Quart. J. Econom. 75(4):643–669.CrossrefGoogle Scholar
  • Epstein LG, Schneider M (2003) Recursive multiple-priors. J. Econom. Theory 113(1):1–31.CrossrefGoogle Scholar
  • Epstein LG, Schneider M (2007) Learning under ambiguity. Rev. Econom. Stud. 74(4):1275–1303.CrossrefGoogle Scholar
  • Epstein LG, Schneider M (2008) Ambiguity, information quality and asset pricing. J. Finance 63(1):197–228.CrossrefGoogle Scholar
  • Epstein LG, Schneider M (2010) Ambiguity and asset markets. Annual Rev. Financial Econom. 2:315–346.CrossrefGoogle Scholar
  • Fudenberg D, Strack P, Strzalecki T (2018) Speed accuracy and the optimal timing of choices. Amer. Econom. Rev. 108(2):3651–3684.CrossrefGoogle Scholar
  • Gilboa I (2009) Theory of Decision Under Uncertainty (Cambridge University Press, New York).CrossrefGoogle Scholar
  • Gilboa I (2015) Rationality and the Bayesian paradigm. J. Econom. Methods 22(3):312–334.CrossrefGoogle Scholar
  • Gilboa I, Schmeidler D (1989) Maxmin expected utility with non-unique prior. J. Math. Econom. 18(2):141–153.CrossrefGoogle Scholar
  • Gilboa I, Postlewaite A, Schmeidler D (2012) Rationality of belief or: Why Savage’s axioms are neither necessary nor sufficient for rationality. Synthese 187(1):11–31.CrossrefGoogle Scholar
  • Howard RA (1970) Decision analysis: Perspectives on inference, decision, and experimentation. Proc. IEEE 58(5):632–643.CrossrefGoogle Scholar
  • Huang YJ, Nguyen-Huu A, Zhou XY (2020) General stopping behaviors of naive and non-committed sophisticated agents, with application to probability distortion. Math. Finance 30(1):310–340.Google Scholar
  • Huber PJ (1965) A robust version of the probability ratio test. Ann. Math. Statist. 36(6):1753–1758.CrossrefGoogle Scholar
  • Kadane JB, Schervish MJ, Seidenfeld T (1996) Reasoning to a foregone conclusion. JASA 91(435):1228–1235.CrossrefGoogle Scholar
  • Li J (2019) The K-armed bandit problem with multiple-priors. J. Math. Econom. 80(1):22–38.CrossrefGoogle Scholar
  • Liptser R, Shiryaev A (1977) Statistics of Random Processes I: General Theory (Springer, Berlin).CrossrefGoogle Scholar
  • Marinacci M (2002) Learning from ambiguous urns. Statist. Papers 43(1):143–151.CrossrefGoogle Scholar
  • Miao J (2009) Ambiguity, risk and portfolio choice under incomplete information. Ann. Econom. Finance 10(2):257–279.Google Scholar
  • Oksendal B (2005) Stochastic Differential Equations, 6th ed. (Springer, Berlin).Google Scholar
  • Peskir G (2017) Nonlinear optimal stopping and nonlinear optimal control. Presentation, Conference on Optimal Stopping in Complex Environments, Bielefeld, Germany.Google Scholar
  • Peskir G, Shiryaev A (2006) Optimal Stopping and Free-Boundary Problems (Springer, Berlin).Google Scholar
  • Rios-Insua D, Ruggeri F (2000) Robust Bayesian Analysis (Springer, New York).CrossrefGoogle Scholar
  • Shapiro A (2016) Rectangular sets of probability measures. Oper. Res. 64(2):528–541.LinkGoogle Scholar
  • Shiryaev A (2008) Optimal Stopping Rules, 2nd ed. Aries AB, trans. (Springer, Berlin).Google Scholar
  • Trautman ST, Zeckhauser RJ (2013) Shunning uncertainty: The neglect of learning opportunities. Games Econom. Behav. 79:44–55.CrossrefGoogle Scholar
  • Wald A (1945) Sequential tests of statistical hypotheses. Ann. Math. Statist. 16(2):117–186.CrossrefGoogle Scholar
  • Wald A (1947) Sequential Analysis (Wiley, New York).Google Scholar
  • Walley P (1991) Statistical Reasoning with Imprecise Probabilities (Chapman and Hall, London).CrossrefGoogle Scholar
  • Zhang J (2017) Backward Stochastic Differential Equations (Springer, New York).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.