Денис Беломестный: “Вычислительная разрешимость задач оптимальной остановки”
27 февраля в МШЭ МГУ состоялось очередное заседание Глобального онлайн семинара “Финансовая математика”. Страница семинара.
На семинаре выступил Денис Беломестный из университета Дуйсбурга-Эссена (Германия) с докладом на тему “Вычислительная разрешимость задач оптимальной остановки”. https://disk.yandex.ru/i/5ztbShoaJK24Cg.
Из аннотации:
In this paper, we propose a Weighted Stochastic Mesh (WSM) algorithm for approximating the value of discrete- and continuous-time optimal stopping problems. In this context, we consider tractability of such problems via a useful notion of semitractability and the introduction of a tractability index for a particular numerical solution algorithm. It is shown that in the discrete-time case the WSM algorithm leads to semitractability of the corresponding optimal stopping problem in the sense that its complexity is bounded in order by −4 log +2(1∕ ) with being the dimension of the underlying Markov chain. Furthermore, we study the WSM approach in the context of continuous-time optimal stopping problems and derive the сorresponding complexity bounds. Although we cannot prove semi-tractability in this case, our bounds turn out to be the tightest ones among the complexity bounds known in the literature. We illustrate our theoretical findings by a numerical example.