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Solution of Optimal Stopping Problem Based on a Modification of Payoff Function

In: Inspired by Finance

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  • Ernst Presman

    (Russian Academy of Sciences (RAS), Central Economics and Mathematics Institute (CEMI))

Abstract

An optimal stopping problem of a Markov process with infinite horizon is considered. For the case of discrete time and finite number m of states Sonin proposed an algorithm which allows to find the value function and the stopping set in no more than 2(m−1) steps. The algorithm is based on a modification of a Markov chain on each step, related to the elimination of the states which definitely belong to the continuation set. To solve the problem with arbitrary state space and to have possibility of a generalization to a continuous time, the procedure was modified in Presman (Stochastics 83(4–6):467–475, 2011). The modified procedure was based on a sequential modification of the payoff function for the same chain in such a way that the value function is the same for both problems and the modified payoff function is greater than the initial one on some set and is equal to it on the complement. In this paper, we give some examples showing that the procedure can be generalized to continuous time.

Suggested Citation

  • Ernst Presman, 2014. "Solution of Optimal Stopping Problem Based on a Modification of Payoff Function," Springer Books, in: Yuri Kabanov & Marek Rutkowski & Thaleia Zariphopoulou (ed.), Inspired by Finance, edition 127, pages 505-517, Springer.
    • Handle: RePEc:spr:sprchp:978-3-319-02069-3_23
    DOI: 10.1007/978-3-319-02069-3_23
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