Mathematical Modelling of Liquidity Risk in Financial Markets

在金融市场中，股票、债券或商品等资产在以下情况下被称为非流动性资产：无法在任何预期时间进行大量交易（买方和卖方并不总是可用）;大量交易的额外成本或流动性溢价不可忽略;或大宗交易对价格的影响持续一段时间。当流动性水平随时间随机变化时，流动性就成为一个风险因素。近年来，限价订单簿数据的可用性使流动性风险成为全球许多交易部门的焦点。从数学模型的角度来看，只有最后两个方面的非流动性已被认为是在学术文献的细节。此外，这两个概念通常被区别对待，很少有人把它们联系起来。在文献中，人们多次发现，一个现实的模型，只有当它正确地整合了流动性的所有维度，才能导致现实的解决方案。该研究计划的广泛目标是根据实际中可以观察或估计的数量开发流动性三个维度的有用数学模型，并通过考虑各种定价和最优投资组合问题来研究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.******