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Stochastics
An International Journal of Probability and Stochastic Processes
Volume 96, 2024 - Issue 1
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Research Article

Risk-sensitive discounted Markov decision processes with unbounded reward functions and Borel spaces

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Pages 649-666 | Received 22 May 2023, Accepted 31 Jan 2024, Published online: 12 Mar 2024

References

  • N. Bäuerle and A. Jaśkiewicz, Risk-sensitive dividend problems, Europ. J. Oper. Res. 242 (2015), pp. 161–171.
  • N. Bäuerle and U. Rieder, More risk-sensitive Markov decision processes, Math. Oper. Res. 39 (2014), pp. 105–120.
  • N. Bauerle and U. Rieder, Partially observable risk-sensitive Markov decision processes, Math. Oper. Res. 42 (2017), pp. 1180–1196.
  • T. Bielecki, D. Hernández-Hernández, and S.R. Pliska, Risk sensitive control of finite state Markov chains in discrete time, with applications to portfolio management, Math. Methods Oper. Res. 50 (1999), pp. 167–188.
  • V.S. Borkar and S.P. Meyn, Risk-sensitive optimal control for Markov decision processes with monotone cost, Math. Oper. Res. 27 (2002), pp. 192–209.
  • G.B. Di Masi and L. Stettner, Risk-sensitive control of discrete-time Markov processes with infinite horizon, SIAM J. Control Optim. 38 (1999), pp. 61–78.
  • G.B. Di Masi and L. Stettner, Infinite horizon risk-sensitive control of discrete time Markov processes under minorization property, SIAM J. Control Optim. 46 (2007), pp. 231–252.
  • M.K. Ghosh and S. Saha, Risk-sensitive control of continuous time Markov chains, Stochastics. 86 (2014), pp. 655–675.
  • X. Guo, Q.L. Liu, and Y. Zhang, Finite horizon risk-sensitive continuous-time Markov decision processes with unbounded transition and cost rates, 4OR 17 (2019), pp. 427–442.
  • X.P. Guo and Z.W. Liao, Risk-sensitive discounted continuous-time Markov decision processes with unbounded rates, SIAM J. Control Optim. 57 (2019), pp. 3857–3883.
  • O. Hernández-Lerma and J.B. Lasserre, Further Topics on Discrete-Time Markov Control Processes, Springer-Verlag, New York, 1999.
  • S.C. Jaquette, A utility criterion for Markov decision processes, Management Sci. 23 (1976), pp. 43–49.
  • A. Jaśkiewicz, Average optimality for risk-sensitive control with general state space, Ann. Appl. Probab. 17 (2007), pp. 654–675.
  • A.S. Nowak, Measurable selection theorems for minimax stochastic optimization problems, SIAM J. Control Optim. 23 (1985), pp. 466–476.
  • K. Suresh Kumar and P. Chandan, Risk-sensitive control of pure jump process on countable space with near monotone cost, Appl. Math. Optim. 68 (2013), pp. 311–331.
  • Q.D. Wei, Continuous-time Markov decision processes with risk-sensitive finite-horizon cost criterion, Math. Meth. Oper. Res. 84 (2016), pp. 461–487.
  • Y. Zhang, Continuous-time Markov decision processes with exponential utility, SIAM J. Control Optim 55 (2017), pp. 2636–2660.

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