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An iterative method for multiple stopping: convergence and stability

Part of: Stochastic processes Sequential methods

Published online by Cambridge University Press:  01 July 2016

Christian Bender  and
John Schoenmakers
Christian Bender*
Affiliation:
Weierstrass Institute for Applied Analysis and Stochastics
John Schoenmakers*
Affiliation:
Weierstrass Institute for Applied Analysis and Stochastics
*
∗ Postal address: Weierstrass Institute for Applied Analysis and Stochastics, Mohrenstr. 39, D-10117 Berlin, Germany.
∗ Postal address: Weierstrass Institute for Applied Analysis and Stochastics, Mohrenstr. 39, D-10117 Berlin, Germany.
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Abstract

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We present a new iterative procedure for solving the multiple stopping problem in discrete time and discuss the stability of the algorithm. The algorithm produces monotonically increasing approximations of the Snell envelope which coincide with the Snell envelope after finitely many steps. Unlike backward dynamic programming, the algorithm allows us to calculate approximative solutions with only a few nestings of conditional expectations and is, therefore, tailor-made for a plain Monte Carlo implementation.

Keywords

Optimal stoppingpolicy improvementmultiple callable financial derivatives

MSC classification

Primary: 60G40: Stopping times; optimal stopping problems; gambling theory 62L15: Optimal stopping

Information

Type
General Applied Probability
Information
Advances in Applied Probability , Volume 38 , Issue 3 , September 2006 , pp. 729 - 749
Copyright
Copyright © Applied Probability Trust 2006 

Footnotes

Supported by the DFG Research Center Matheon, Berlin.

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