Dynamic Programming in Ordered Vector Space

Published Online:https://doi.org/10.1287/opre.2025.1971

References

  • Aliprantis CD, Border KC (2006) Infinite Dimensional Analysis: A Hitchhiker’s Guide (Springer, Berlin).Google Scholar
  • Bäuerle N, Glauner A (2022) Markov decision processes with recursive risk measures. Eur. J. Oper. Res. 296(3):953–966.CrossrefGoogle Scholar
  • Bäuerle N, Jaśkiewicz A (2018) Stochastic optimal growth model with risk sensitive preferences. J. Econom. Theory 173:181–200. CrossrefGoogle Scholar
  • Bäuerle N, Jaśkiewicz A (2024) Markov decision processes with risk-sensitive criteria: An overview. Math. Methods Oper. Res. 99(1):141–178.CrossrefGoogle Scholar
  • Bäuerle N, Rieder U (2011) Markov Decision Processes with Applications to Finance (Springer, Berlin).CrossrefGoogle Scholar
  • Bäuerle N, Jaśkiewicz A, Nowak AS (2021) Stochastic dynamic programming with non-linear discounting. Appl. Math. Optim. 84(3):2819–2848.CrossrefGoogle Scholar
  • Bellman R (1957) Dynamic Programming (Princeton University Press, Princeton, NJ).Google Scholar
  • Bertsekas D (2012) Dynamic Programming and Optimal Control, 4th ed., vol. I (Athena Scientific, Belmont, MA).Google Scholar
  • Bertsekas D (2021) Rollout, Policy Iteration, and Distributed Reinforcement Learning (Athena Scientific, Belmont, MA).Google Scholar
  • Bertsekas D (2022) Abstract Dynamic Programming (Athena Scientific, Belmont, MA).Google Scholar
  • Bloise G, Le Van C, Vailakis Y (2024) Do not blame Bellman: It is Koopmans’ fault. Econometrica 92(1):111–140.CrossrefGoogle Scholar
  • Brenner S (2015) The risk preferences of U.S. executives. Management Sci. 61(6):1344–1361.LinkGoogle Scholar
  • Davey BA, Priestley HA (2002) Introduction to Lattices and Order (Cambridge University Press, Cambridge, UK).CrossrefGoogle Scholar
  • de Castro L, Galvao AF (2019) Dynamic quantile models of rational behavior. Econometrica 87(6):1893–1939.CrossrefGoogle Scholar
  • de Castro L, Galvao AF (2022) Static and dynamic quantile preferences. Econom. Theory 73(2–3):747–779.CrossrefGoogle Scholar
  • de Castro L, Galvao AF, Nunes D (2025) Dynamic economics with quantile preferences. Theoret. Econom. 20(1):353–425.CrossrefGoogle Scholar
  • Giovannetti BC (2013) Asset pricing under quantile utility maximization. Rev. Financial Econom. 22(4):169–179.CrossrefGoogle Scholar
  • Graham JR, Harvey CR, Puri M (2013) Managerial attitudes and corporate actions. J. Financial Econom. 109(1):103–121.CrossrefGoogle Scholar
  • Hills TS, Nakata T, Schmidt S (2019) Effective lower bound risk. Eur. Econom. Rev. 120:103321.CrossrefGoogle Scholar
  • Jaśkiewicz A, Matkowski J, Nowak AS (2014) On variable discounting in dynamic programming: Applications to resource extraction and other economic models. Ann. Oper. Res. 220:263–278.CrossrefGoogle Scholar
  • Kamihigashi T, Stachurski J (2012) An order-theoretic mixing condition for monotone Markov chains. Statist. Probab. Lett. 82(2):262–267.CrossrefGoogle Scholar
  • Kamihigashi T, Stachurski J (2014) Stochastic stability in monotone economies. Theoret. Econom. 9(2):383–407.CrossrefGoogle Scholar
  • Kantorovich L (1939) The method of successive approximation for functional equations. Acta Math. 71(1):63–97.CrossrefGoogle Scholar
  • Kochenderfer MJ, Wheeler TA, Wray KH (2022) Algorithms for Decision Making (MIT Press, Cambridge, MA).Google Scholar
  • Koudstaal M, Sloof R, Van Praag M (2016) Risk, uncertainty, and entrepreneurship: Evidence from a lab-in-the-field experiment. Management Sci. 62(10):2897–2915.LinkGoogle Scholar
  • Maccheroni F, Marinacci M, Rustichini A (2006) Dynamic variational preferences. J. Econom. Theory 128(1):4–44.CrossrefGoogle Scholar
  • Marinacci M, Montrucchio L (2010) Unique solutions for stochastic recursive utilities. J. Econom. Theory 145(5):1776–1804.CrossrefGoogle Scholar
  • Marinacci M, Montrucchio L (2019) Unique Tarski fixed points. Math. Oper. Res. 44(4):1174–1191.LinkGoogle Scholar
  • Murphy K (2024) Reinforcement learning: An overview. Preprint, submitted December 6, https://arxiv.org/abs/2412.05265.Google Scholar
  • Puterman ML (2005) Markov Decision Processes: Discrete Stochastic Dynamic Programming (Wiley, New York).Google Scholar
  • Sargent TJ, Stachurski J (2025) Dynamic programs on partially ordered sets. SIAM J. Control Optim. 63(2):778–795.CrossrefGoogle Scholar
  • Schwartz J (1954) The formula for change in variables in a multiple integral. Amer. Math. Monthly 61(2):81–85.CrossrefGoogle Scholar
  • Stachurski J, Zhang J (2021) Dynamic programming with state-dependent discounting. J. Econom. Theory 192:105190.CrossrefGoogle Scholar
  • Tauchen G (1986) Finite state Markov-chain approximations to univariate and vector autoregressions. Econom. Lett. 20(2):177–181.CrossrefGoogle Scholar
  • Toda AA (2024) Unbounded Markov dynamic programming with weighted supremum norm Perov contractions. Econom. Theory Bull. 12(2):141–156.CrossrefGoogle Scholar
  • Veldkamp L (2023) Valuing data as an asset. Rev. Finance 27(5):1545–1562.CrossrefGoogle Scholar
  • Zaanen AC (2012) Introduction to Operator Theory in Riesz Spaces (Springer, Berlin).Google 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.