Maximum likelihood estimation of the parameters of stochastic differential equations

本计画的主要目标是发展有效的演算法，以利用模拟极大似然法与精确极大似然法来估计随机微分方程的参数。该研究将以新颖的方式利用参数和非参数分析来构建计算上可行的估计程序。然后，这些方法将应用于金融领域，并用于估计随机波动模型的参数，从而有助于了解复杂系统的一个重要领域，即金融风险。该合作项目的执行将提供数学金融专题领域的高质量研究培训，并培养高素质的研究生。

The primary objective of this project is to develop efficient algorithms for estimating the parameters of stochastic differential equations (SDEs) by simulated and exact maximum likelihood. The research will draw on both parametric and non-parametric analysis in novel ways to construct estimation procedures that are computationally feasible. These methods will then be applied in the area of finance and used to estimate the parameters of stochastic-volatility models, thus contributing to knowledge in a prominent area of complex systems, namely financial risk. The execution of this collaborative project will deliver quality research training in the topical area of mathematical finance and produce high-calibre postgraduates.