Please use this identifier to cite or link to this item: http://hdl.handle.net/10419/233754
Authors: 
Belomestny, Denis
Kaledin, Maxim
Schoenmakers, John
Year of Publication: 
2020
Citation: 
[Journal:] Mathematical Finance [ISSN:] 1467-9965 [Volume:] 30 [Issue:] 4 [Pages:] 1591-1616
Abstract: 
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 ε−4logd+2(1/ε) with d 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 corresponding complexity bounds. Although we cannot prove semitractability 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.
Subjects: 
American options
complexity
Monte Carlo algorithms
optimal stopping
Persistent Identifier of the first edition: 
Creative Commons License: 
http://creativecommons.org/licenses/by/4.0/
Document Type: 
Article
Document Version: 
Published Version

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