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[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.]
Published: Jun 27, 2018
Keywords: Singular control; Impulse control; Zero-sum games; Optimal stopping; Spectrally one-sided Lévy processes; Scale functions; 60G51; 93E20; 49J40
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