Advanced Simulation-Based Methods for Optimal Stopping and Control by Denis Belomestny & John Schoenmakers

Author:Denis Belomestny & John Schoenmakers
Language: eng
Format: epub
Publisher: Palgrave Macmillan UK, London

(10.9)

with the convention that for , , and for , .

Proposition 90

We have the following Bellman type reduction principle

(10.10)

Proof

This can be proved straightforwardly by induction.

This proposition may also be considered as a discrete time version of a related continuous time result in the setting of [72]. Thanks to Proposition 90 and standard results on single stopping problems we observe that a family of optimal stopping times for (10.8) is given recursively by

for

Remark 91

The following slight generalization of a Doob martingale will be useful later on. We say that a martingale is a Doob martingale of whenever there exists a predictable process such that is -measurable for any . In particular, for any two Doob martingales and of it holds

Download

Copyright Disclaimer:
This site does not store any files on its server. We only index and link to content provided by other sites. Please contact the content providers to delete copyright contents if any and email us, we'll remove relevant links or contents immediately.