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Martingale Approach to Stochastic Control with Discretionary Stopping |
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| Authors: | Ioannis Karatzas Ingrid-Mona Zamfirescu |
| Affiliation: | (1) Departments of Mathematics and Statistics, 619 Mathematics Building, Columbia University, MC 4438, New York, NY 10027, USA;(2) Department of Mathematics, Baruch College, CUNY, New York, NY 10010, USA |
| 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. |
| Keywords: | Stochastic control Optimal stopping Martingales Doob-Meyer decompositions |
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