Abstract
We consider an ergodic stochastic control problem for a class of one‐dimensional Itô processes where the available control is an added bounded variation process. The corresponding infinite horizon discounted control problem was solved in [A. Weerasinghe, SIAM J. Control Optim., 44 (2005), pp. 389–417]. Here, we show that as the discount factor approaches zero, the optimal strategies derived in [A. Weerasinghe, SIAM J. Control Optim., 44 (2005), pp. 389–417] “converge” to an optimal strategy for the ergodic control problem. Under different assumptions, two types of optimal strategies were derived. Also, the Abelian limit relationships among the ergodic control problem, the infinite horizon discounted control problem, and the finite time horizon control problem are established here. A solution to a constrained optimization problem is obtained as an application.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.