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Optimality of Two-Parameter Strategies in Stochastic Control

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XII Symposium of Probability and Stochastic Processes

Part of the book series: Progress in Probability ((PRPR,volume 73))

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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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Acknowledgements

The author thanks the anonymous referee for constructive comments and suggestions. K. Yamazaki is supported by MEXT KAKENHI Grant Number 26800092 and 17K05377.

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Authors and Affiliations

  1. Department of Mathematics, Faculty of Engineering Science, Kansai University, Suita-shi, Osaka, Japan

    Kazutoshi Yamazaki

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  1. Kazutoshi Yamazaki
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Correspondence to Kazutoshi Yamazaki .

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Editors and Affiliations

  1. Department of Probability and Statistics, Center for Research in Mathematics, Guanajuato, Mexico

    Daniel Hernández-Hernández

  2. Department of Probability and Statistics, Center for Research in Mathematics, Guanajuato, Mexico

    Juan Carlos Pardo

  3. Department of Probability and Statistics, Center for Research in Mathematics, Guanajuato, Mexico

    Victor Rivero

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Yamazaki, K. (2018). Optimality of Two-Parameter Strategies in Stochastic Control. In: Hernández-Hernández, D., Pardo, J., Rivero, V. (eds) XII Symposium of Probability and Stochastic Processes. Progress in Probability, vol 73. Birkhäuser, Cham. https://doi.org/10.1007/978-3-319-77643-9_2

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