On a class of singular stochastic control problems for reflected diffusions

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:473

Article

Ferrari, Giorgio¹ 

[1] Bielefeld Univ, Ctr Math Econ IMW, Univ Str 25, D-33615 Bielefeld, Germany

关键词: Reflected one-dimensional diffusions;    Singular stochastic control;    Variational inequality;    Optimal stopping;    Optimal dividend;    Optimal harvesting;   

DOI  :  10.1016/j.jmaa.2019.01.004

来源: Elsevier

【 摘 要 】

Reflected diffusions naturally arise in many problems from applications ranging from economics and mathematical biology to queueing theory. In this paper, we consider a class of infinite time-horizon singular stochastic control problems for a general one-dimensional diffusion that is reflected at zero. We assume that exerting control leads to a state-dependent instantaneous reward, whereas reflecting the diffusion at zero gives rise to a proportional cost with constant marginal value. The aim is to maximize the total expected reward, minus the total expected cost of reflection. We show that depending on the properties of the state-dependent instantaneous reward we can have qualitatively different kinds of optimal strategies. The techniques employed are those of stochastic control and of the theory of linear diffusions. (C) 2019 Elsevier Inc. All rights reserved.

【 授权许可】

Free