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A Near-Optimal Selling Rule for a Two-Time-Scale Market Model

This paper is concerned with a near-optimal stock selling rule. The salient features include the use of a switching geometric Brownian motion model and two-time-scale formulation. The factor (switching) process is modeled as a continuous-time Markov chain with a finite state space. A key feature of the model is that the Markov chain has a large state space. Although it has been established that the optimal selling rule can be obtained by solving a system of two-point boundary value problems, the computational complexity may become a real issue. In this paper, to overcome the difficulty, a multiscale model is proposed, and a near-optimal strategy is developed using an associated limit problem and the multiscale structure of the underlying system. After ensuring the existence and uniqueness of the system of two-point boundary value problems, in addition to deriving the target price and the stop-loss limit, profit probability, loss probability, expected exit time, and expected holding time are computed. It i...