Abstract
In this paper we develop two numerical methods for optimal stopping in the framework of one dimensional diffusion. Both of the methods use the Skorokhod embedding in order to construct recombining tree approximations for diffusions with general coefficients. This technique allows us to determine convergence rates and construct nearly optimal stopping times which are optimal at the same rate. Finally, we demonstrate the efficiency of our schemes on several models.
| Original language | American English |
|---|---|
| Pages (from-to) | 602-633 |
| Number of pages | 32 |
| Journal | SIAM Journal on Financial Mathematics |
| Volume | 9 |
| Issue number | 2 |
| DOIs | |
| State | Published - 2018 |
Bibliographical note
Funding Information:∗Received by the editors February 28, 2017; accepted for publication (in revised form) December 12, 2017; published electronically May 8, 2018. http://www.siam.org/journals/sifin/9-2/M111886.html Funding: The work of the first author was supported in part by the National Science Foundation under grant DMS-1613170 and by the Susan M. Smith Professorship. The work of the second author was supported by supported by Marie Curie Career Integration grant 618235 and the ISF grant 160/17. †Department of Mathematics, University of Michigan, Ann Arbor, MI 48109 (erhan@umich.edu, guojia@umich. edu). ‡Department of Statistics, Hebrew University, Jerusalem, Israel, and School of Mathematical Sciences, Monash University (yan.dolinsky@mail.huji.ac.il).
Funding Information:
The work of the first author was supported in part by the National Science Foundation under grant DMS-1613170 and by the Susan M. Smith Professorship. The work of the second author was supported by supported by Marie Curie Career Integration grant 618235 and the ISF grant 160/17.
Publisher Copyright:
© 2018 Society for Industrial and Applied Mathematics.
Keywords
- American options
- Optimal stopping
- Recombining trees
- Skorohkhod embedding