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A finite horizon optimal switching problem with memory and application to controlled SDDEs

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  • Magnus Perninge

    (Linnaeus University)

Abstract

We consider an optimal switching problem where the terminal reward depends on the entire control trajectory. We show existence of an optimal control by applying a probabilistic technique based on the concept of Snell envelopes. We then apply this result to solve an impulse control problem for stochastic delay differential equations driven by a Brownian motion and an independent compound Poisson process. Furthermore, we show that the studied problem arises naturally when maximizing the revenue from operation of a group of hydro-power plants with hydrological coupling.

Suggested Citation

  • Magnus Perninge, 2020. "A finite horizon optimal switching problem with memory and application to controlled SDDEs," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 91(3), pages 465-500, June.
    • Handle: RePEc:spr:mathme:v:91:y:2020:i:3:d:10.1007_s00186-019-00699-1
    DOI: 10.1007/s00186-019-00699-1
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    References listed on IDEAS

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