Mathematical Modelling of Liquidity Risk in Financial Markets

在金融市场中，当大量交易不能总是在任何期望的时间进行交易时(买家和卖家并不总是可用的)，当大量交易的额外成本或流动性溢价不可忽略时，或者当一笔大额交易对价格的影响随着时间的推移持续存在时，股票、债券或大宗商品等资产被称为非流动性资产。当流动性水平在时间上随机演变时，流动性就成为一个风险因素。近年来，限价指令账簿数据的可获得性使流动性风险成为全球许多交易部门关注的焦点。从数学模型的角度来看，只有流动性不足的最后两个维度在学术文献中得到了详细的考虑。此外，这两个概念通常被区别对待，它们之间几乎没有什么联系。在文献中多次发现，一个现实的模型只有在适当地整合流动性的所有维度时才能产生现实的解决方案。这一研究计划的广泛目标是，根据在实践中可以观察或估计的数量，开发一个关于流动性的三个维度的有用的数学模型，并通过考虑各种定价和最优投资组合问题来调查每个维度的关系和影响。

In financial markets, an asset such as a stock, a bond or a commodity is said to be illiquid when large quantities cannot always be traded at any desired time (buyers and sellers are not always available), when the added cost of trading large quantities, or liquidity premium, is non-negligible, or when the impact of a large transaction on prices persists over time. Liquidity becomes a risk factor when its level evolves randomly in time. In recent years, the availability of limit order book data has made liquidity risk the focal point of many trading desks around the world. From a mathematical modelling point of view, only the last two dimensions of illiquidity have been considered in details in the academic literature. Furthermore, these two notions have usually been**treated very differently and few connections have been made between them. Many times in the literature, it has been found that a realistic model can lead to realistic solutions only if it properly integrates all dimensions of liquidity. The broad objective of this research program is to develop a useful mathematical model of the three dimensions of liquidity based on quantities that can be observed or estimated in practice and investigate the relations and the impact of each dimension by considering various pricing and optimal portfolio problems.******