Stationary Distribution Of Markov-modulated Reflected Ornstein-Uhlenbeck Process

The refected Markov-modulated models have been widely used in such prac-tical issues as queueing networks, operation research, the evaluation of fnancialrisk and the modeling of regulated fnancial markets.Given the literature concern-ing refected Markov-modulated models, they are mainly concerned with refectedMarkov-modulated Brownian motions (RMMBM). However, as a more general mod-el compared with RMMBM, Ornstein-Uhlenbeck processes have become one of themost important models for describing fuid queue and the term structure of interestrates.In this paper, we focus on a class of Markov-modulated Ornstein-Uhlenbeckprocesses with double-sided jumps and two-sides refected barriers. The jump isdescribed as a Markov-modulated compound Poisson process, and the jump size issupposed to satisfy a double-exponential distribution. Moreover, the drift, difusivecoefcients and the jumps are modulated by a continuous time fnite state spacehomogeneous irreducible Markov chain.The main contribution of this paper is to show that the stationary distributionof the refected process satisfes an interacting ordinary integro-diferential equa-tion. Then the existence and uniqueness of solution to the interacting equation arediscussed when the Markov chain has two states. Moreover, we consider the nu-merical solution to this interacting integro-diferential equation by employing fnitediference method, and fnally present the sensitivity of the stationary distributionw.r.t. the various model parameters.