A D-Solution Of A Multi-Parameter Continuous Time Optimal Stopping Problem With Constraints

In this paper, a continuous time optimal stopping problem with general constraints is investigated. The Lagrangian programming problem associated with the original optimal stopping problem is given. Furthermore in order to use convex analysis and deterministic optimization theory, the concept of a weak optimal tactic in addition to an optimal tactic is introduced. Under the non-atomic probability measure and the condition corresponding to the Slater condition in the nonlinear programming theory, the relation between an optimal tactic and a weak optimal tactic and the existence of an optimal tactic are shown. Finally by using perturbing the original optimal stopping problem, the Lagrangian duality theory is developed.