采用马尔科夫链逼近的方法研究了在股票交易中的最佳清算准则的数值算法.与现有文献相比,文章具有以下特点:首先,不同于基于布朗运动的股票模型,我们采用由连续时间马尔科夫链驱动的动态模型.其次,我们着重解决大宗股票的交易问题.和我们之前文章中通过动态规划把相应的问题转化为带状态约束的HJB (Hamilton-Jacobi-Bellman)方程的方法略有不同,我们采取马尔科夫链逼近的方法,对数值算法的收敛性进行了论证.此外,我们进一步提供了相应的数值实例用以演示说明.

This work develops a numerical approximation procedure based on Markov chain approximation methods for optimal liquidation rules of stock trading. There are several distinct features compared to the existing literature. First, in lieu of a Brownian motion based model, our formulation uses a model driven by a continuous-time Markov chain. Second, in this work, we focus on finding the liquidation strategies for a large block stock. Accommodating our recent work using a dynamic programming approach that leads to the associate HJB (Hamilton-Jacobi-Bellman) equations with state constraints, this work establishes the convergence of the associated numerical algorithms using a Markov chain approximation approach. In addition, an example is provided for demonstration purpose.