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Published in:
Scaling Limits of Markov-Branching Trees and Applications Read chapter Read first chapter

2018 | OriginalPaper | Chapter

Optimality of Two-Parameter Strategies in Stochastic Control

Author : Kazutoshi Yamazaki

Published in: XII Symposium of Probability and Stochastic Processes

Publisher: Springer International Publishing

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Abstract

In this note, we study a class of stochastic control problems where the optimal strategies are described by two parameters. These include a subset of singular control, impulse control, and two-player stochastic games. The parameters are first chosen by the two continuous/smooth fit conditions, and then the optimality of the corresponding strategy is shown by verification arguments. Under the setting driven by a spectrally one-sided Lévy process, these procedures can be efficiently performed owing to the recent developments of scale functions. In this note, we illustrate these techniques using several examples where the optimal strategy and the value function can be concisely expressed via scale functions.

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previous chapter Scaling Limits of Markov-Branching Trees and Applications
next chapter Asymptotic Results for the Severity and Surplus Before Ruin for a Class of Lévy Insurance Processes
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Metadata
Title
Optimality of Two-Parameter Strategies in Stochastic Control
Author
Kazutoshi Yamazaki
Copyright Year
2018
Book
XII Symposium of Probability and Stochastic Processes

Print ISBN: 978-3-319-77642-2

Electronic ISBN: 978-3-319-77643-9

Copyright Year: 2018

DOI
https://doi.org/10.1007/978-3-319-77643-9_2