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Optimal switching between a pair of Brownian motions

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Mathematics in Industrial Problems

Part of the book series: The IMA Volumes in Mathematics and Its Applications ((IMA,volume 24))

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Abstract

Although engineering models are concerned with multi-step decision making in discrete time, the continuous analog may provide a good insight as well as a good approximation. Here we deal with the situation where a number of controlled processes are available, and one is allowed to switch from one process to another; the goal is to maximize a certain payoff which depends on those processes chosen by the switching mechanism. This type of problem occurs in dynamic allocation of resources (cf. armed bandit problems [1]), in supply and demand strategies [2], etc. We shall deal here with the case where the control mechanism can switch from one diffusion process to another in any non-anticipative way and with no penalty. This problem was studied by N.V. Krylov in a sequence of papers during the 1970’s; his results are described in detail in his book [3].

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References

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Authors and Affiliations

  1. Institute for Mathematics and Its Applications, University of Minnesota, 55455, Minneapolis, MN, USA

    Avner Friedman (Director)

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  1. Avner Friedman
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© 1989 Springer-Verlag New York Inc.

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Friedman, A. (1989). Optimal switching between a pair of Brownian motions. In: Mathematics in Industrial Problems. The IMA Volumes in Mathematics and Its Applications, vol 24. Springer, New York, NY. https://doi.org/10.1007/978-1-4615-7402-6_13

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  • DOI: https://doi.org/10.1007/978-1-4615-7402-6_13

  • Publisher Name: Springer, New York, NY

  • Print ISBN: 978-1-4615-7404-0

  • Online ISBN: 978-1-4615-7402-6

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