论文标题
一种半马多维亚的方法，用于建模股票价格的滴答动态
A semi-Markovian approach to model the tick-by-tick dynamics of stock price
论文作者
论文摘要
我们通过使用Poisson随机度量获得的半马尔可夫过程对股票价格动态进行建模。我们确定了非均匀终端价值问题的经典解决方案的存在和独特性，我们表明，可以作为线性偏微分方程的经典解决方案获得的股票价格的预期值，这是本文研究的终端值问题的特殊情况。我们使用代理商的观点进一步分析了市场制造问题，该代理商以最优惠的价格发布了限额订单。我们使用动态编程原理来获得HJB方程。在无风险厌恶的情况下，我们获得了值函数作为线性PDE的经典解，并通过求解HJB方程来得出最佳控制的表达式。
We model the stock price dynamics through a semi-Markov process obtained using a Poisson random measure. We establish the existence and uniqueness of the classical solution of a non-homogeneous terminal value problem and we show that the expected value of stock price at horizon can be obtained as a classical solution of a linear partial differential equation that is a special case of the terminal value problem studied in this paper. We further analyze the market making problem using the point of view of an agent who posts the limit orders at the best price available. We use the dynamic programming principle to obtain a HJB equation. In no-risk aversion case, we obtain the value function as a classical solution of a linear pde and derive the expressions for optimal controls by solving the HJB equation.
