Optimality of doubly reflected Levy processes in singular control

STOCHASTIC PROCESSES AND THEIR APPLICATIONS

卷:125

Article

Baurdoux, Erik J.¹  Yamazaki, Kazutoshi² 

[1] London Sch Econ, Dept Stat, London WC2A 2AE, England

[2] Kansai Univ, Fac Engn Sci, Dept Math, Suita, Osaka 5648680, Japan

关键词: Singular control;    Doubly reflected Levy processes;    Fluctuation theory;    Scale functions;   

DOI  :  10.1016/j.spa.2015.01.011

来源: Elsevier

【 摘 要 】

We consider a class of two-sided singular control problems. A controller either increases or decreases a given spectrally negative Levy process so as to minimize the total costs comprising of the running and controlling costs where the latter is proportional to the size of control. We provide a sufficient condition for the optimality of a double barrier strategy, and in particular show that it holds when the running cost function is convex. Using the fluctuation theory of doubly reflected Levy processes, we express concisely the optimal strategy as well as the value function using the scale function. Numerical examples are provided to confirm the analytical results. (C) 2015 Elsevier B.V. All rights reserved.

【 授权许可】

Free