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Optional Sampling Theorems

Chapter
Part of the Universitext book series (UTX)

In Chapter 9 we saw that martingales are transformed into martingales if we apply certain admissible gambling strategies. In this chapter, we establish a similar stability property for martingales that are stopped at a random time. In order also to obtain these results for submartingales and supermartingales, in the first section, we start with a decomposition theorem for adapted processes. We show the optional sampling and optional stopping theorems in the second section. The chapter finishes with the investigation of random stopping times with an infinite time horizon.

Keywords

Initial Capital Monotone Convergence Predictable Process Monotone Convergence Theorem Uniform Integrability 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag London Limited 2008

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