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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.)
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