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Markov and semi-Markov decision models and optimal stopping

In: Semi-Markov Models

Author

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  • Manfred Schäl

    (Universität Bonn, Institut für Angewandte Mathematik)

Abstract

We consider a system with a finite number of states i ϵ S. Periodically we observe the current state of the system, and then choose an action a from a set A of possible actions. As a result of the current state i and the chosen action a, the system moves to a new state j with the probability pij (a). As a further consequence, an immediate reward r(i, a) is earned. If the control process is stopped in a state i, then we obtain a terminal reward u (i). Thus, the underlying model is given by a tupel M = (S,A,p,r,u). (i) S stands for the state space and is assumed to be finite. (ii) A is the action space. (iii) pij (a) are the transition probabilities, where Σjϵs pij (a) = 1 for all i ϵ S, a ϵ A. (iv) r (i,a) is the real valued one-step reward. (v) u (i) is the real valued terminal reward or the utility function.

Suggested Citation

  • Manfred Schäl, 1986. "Markov and semi-Markov decision models and optimal stopping," Springer Books, in: Jacques Janssen (ed.), Semi-Markov Models, pages 39-61, Springer.
    • Handle: RePEc:spr:sprchp:978-1-4899-0574-1_4
    DOI: 10.1007/978-1-4899-0574-1_4
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