An optimal stopping problem with a reward constraint
Motivated by financial contracts with equity-trigger protection, the paper studies optimal stopping problems when the set of stopping times is restricted such that the corresponding discounted value at any instant prior to the stopping time exceeds a given threshold \(F\). The authors first focus on the case where the discounted value process is a submartingale, which implies that the corresponding uncontrained problem is stopped optimally only at the end. As may be expected, the constrained problem is solved by the essential supremum of all stopping times in the constraint set. In discrete time the authors consider general payoff processes. In this case the value and the optimal stopping time of the problem are obtaind by a recursion which closely resembles the ordinary unconstrained case. Finally, the continuous-time results are applied to the pricing of corporate claims.
scientific article; zbMATH DE number 6106814
scientific article