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Martingale Approach to Stochastic Control with Discretionary Stopping

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Abstract

We develop a martingale approach for continuous-time stochastic control with discretionary stopping. The relevant Dynamic Programming Equation and Maximum Principle are presented. Necessary and sufficient conditions are provided for the optimality of a control strategy; these are analogues of the "equalization" and "thriftiness" conditions introduced by Dubins and Savage (1976) in a related, discrete-time context. The existence of a thrifty control strategy is established.

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Authors and Affiliations

  1. Departments of Mathematics and Statistics, 619 Mathematics Building, Columbia University, MC 4438, New York, NY 10027, USA

    Ioannis Karatzas

  2. Department of Mathematics, Baruch College, CUNY, New York, NY 10010, USA

    Ingrid-Mona Zamfirescu

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  1. Ioannis Karatzas
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  2. Ingrid-Mona Zamfirescu
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Correspondence to Ioannis Karatzas or Ingrid-Mona Zamfirescu.

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Karatzas, I., Zamfirescu, IM. Martingale Approach to Stochastic Control with Discretionary Stopping. Appl Math Optim 53, 163–184 (2006). https://doi.org/10.1007/s00245-005-0841-2

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  • DOI: https://doi.org/10.1007/s00245-005-0841-2

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