Liquidation of a large block stock under a Markov chain model. (Chinese. English summary) Zbl 1488.91134
Summary: This work develops an optimal liquidation rule for stock trading. There are several distinct features compared to the existing literature. First, in lieu of a Brownian motion based model, a formulation using a continuous-time Markov chain is proposed. Second, in this work, we focus on finding the liquidation strategies for a large block stock. We solve the problem using a dynamic programming approach leading to the associate HJB equations with state constraints. We design a numerical method because a closed-form solution is difficult to obtain. Finally, Two examples are provided for demonstration purpose.
MSC:
91G15 | Financial markets |
91G80 | Financial applications of other theories |
60J20 | Applications of Markov chains and discrete-time Markov processes on general state spaces (social mobility, learning theory, industrial processes, etc.) |