文档介绍
OPTIMAL STOPPING WHEN THE ABSORBING BOUNDARY IS FOLLOWING AFTER MASAHIKO EGAMI AND TADAO ORYU ABSTRACT. We consider a new type of optimal stopping problems where the absorbing boundary moves as the state process X attains new maxima S. More specifically, we set the absorbing boundary as S − b where b is a certain constant. This problem is naturally connected with excursions from zero of the reflected process S − X . We examine this constrained optimization with the state variable X as a spectrally negative ´ Levy process. The problem is in nature a two-dimensional one. The threshold strategy given by the path of just X is not in fact optimal. It turns out, however, that we can reduce the original problem to an infinite number of one-dimensional optimal stopping problems, and we find explicit s