Hidden Markov models for decision analytics

金融数学家工作的最明显和最有用的成果是衍生证券估值、风险管理和资产配置的理论方法和计算方法。研究人员和从业人员在投资交易和金融产品/服务创新中使用这些办法和方法;监管机构也在努力确保资本和金融市场的良好运作。 我的研究小组开发了这样的数学和统计工具，我们专注于使用合适的随机过程调制的隐马尔可夫模型（HALTH）。在上一个授权期间，我们已经提出了一种统一主题的方法来实现HHHT，其中可以完全在线生成模型参数，甚至可以通过高阶HHT（HOHHT）利用先前时间滞后中的信息。在接下来的五年里，我们将通过优先考虑监管，商业和环境中一些当代问题所激发的理论发展和应用，将Hessels提升到实用性，可访问性和多功能性的新水平。特别是，我们将考虑两个问题主题：（1）设计预测分析，包括（a）金融危机的早期预警系统和（B）网络安全风险检测工具;（2）对最近的金融创新进行评估，重点是（a）具有投资担保的保险产品和（B）应用于气候变化适应和灾害风险管理的天气衍生品。在主题（1）中，我们将创建各种扩展的多变量滤波算法的Ornstein-Uhlenbeck和Bessel过程的HOHMM在捕获金融压力指标，并提供在线估计的变化点的结构变化的时间序列数据。我们将采用一种过滤市场方法来处理主题（2），从而生成基于HMM的参数估计将被利用沿着与建设适当的风险中性措施定价合同的复杂功能和支付结构。拟议的研究成果将包括有效的计算方法，在金融工具的估值和对冲，新的和改进的过滤算法的动态参数估计，和定量的解决方案，以当前紧迫的社会问题，使用的组合功率的HOHO和信息融合。这项研究将通过培训高素质的人才，为跨学科和多学科的协同合作开辟更多的途径，提供技术和实践专长。

The most visible and useful outcomes of the work of financial mathematicians are the theoretical approaches and computational methodologies in the valuation of derivative securities, risk management and asset allocation. These approaches and methods are used by researchers and practitioners in investment trading and financial product/service innovations; regulatory agencies use them too in an effort to secure a well-functioning capital and financial markets. My research group develops such mathematical and statistical tools and we specialise in the use of suitable stochastic processes modulated by hidden Markov models (HMMs). Over the previous granting period, we have advanced a unifying-themed approach to HMMs in which one is able to completely generate model parameters online and even take advantage of information in the prior time lags through higher-order HMMs (HOHMMs). In the next five years, we will take HMMs to a new level of utility, accessibility and versatility by prioritising theoretical developments and applications motivated by some contemporary issues in regulation, business, and the environment. In particular, we will consider two problem themes: (1) devise predictive analytics covering (a) early-warning system for financial crisis and (b) cybersecurity-risk detection tools; and (2) perform the valuation of recent financial innovations focusing on (a) insurance products with investment guarantees and (b) weather derivatives with applications to funding climate-change adaptation and disaster risk management. In theme (1), we shall create various extended multivariate filtering algorithms for Ornstein-Uhlenbeck and Bessel processes governed by HOHMM in capturing financial stress indices and provide online estimation for the change points of structural changes in time series data. We will employ a filtered-market methodology to deal with theme (2) whereby generated HMM-based parameter estimates will be utilised along with the construction of appropriate risk-neutral measures for pricing contracts with complex features and payoff structures. Tangible outcomes of the proposed research will include efficient computational methods in the valuation and hedging of financial instruments, new and improved filtering algorithms for dynamic parameter estimation, and quantitative solutions to current pressing societal concerns using the combined power of HOHMMs and information fusion. This research will contribute technical and practical expertise through the training of highly qualified personnel and open more avenues to synergistic collaborations across inter- and multi-disciplinary boundaries.