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On the finite horizon Bellman equation for controlled Markov jump models with unbounded characteristics: existence and approximation

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  • van Dijk, Nico M.

Abstract

This paper studies the finite horizon Bellman equation for controlled Markov jump models with unbounded jump and cost rates. Under concrete growth conditions on the jump rates a method of time-discretization is used to: (i) prove the existence of a solution, (ii) construct a computationally attractive approximation scheme. The accuracy of this scheme is shown to be of linear order. An application to a controlled infinite server is included.

Suggested Citation

  • van Dijk, Nico M., 1988. "On the finite horizon Bellman equation for controlled Markov jump models with unbounded characteristics: existence and approximation," Stochastic Processes and their Applications, Elsevier, vol. 28(1), pages 141-157, April.
    • Handle: RePEc:eee:spapps:v:28:y:1988:i:1:p:141-157
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    Cited by:

    1. Qingda Wei, 2016. "Continuous-time Markov decision processes with risk-sensitive finite-horizon cost criterion," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 84(3), pages 461-487, December.
    2. Sennewald, Ken, 2005. "Controlled Stochastic Differential Equations under Poisson Uncertainty and with Unbounded Utility," Dresden Discussion Paper Series in Economics 03/05, Technische Universität Dresden, Faculty of Business and Economics, Department of Economics.
    3. Qingda Wei, 2017. "Finite approximation for finite-horizon continuous-time Markov decision processes," 4OR, Springer, vol. 15(1), pages 67-84, March.
    4. Sennewald, Ken, 2007. "Controlled stochastic differential equations under Poisson uncertainty and with unbounded utility," Journal of Economic Dynamics and Control, Elsevier, vol. 31(4), pages 1106-1131, April.
    5. Dijk, N.M. van, 1989. "Analytic error bounds for approximations of queueing networks with an application to alternate routing," Serie Research Memoranda 0006, VU University Amsterdam, Faculty of Economics, Business Administration and Econometrics.

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