Hidden Markov models for decision analytics

金融数学家的工作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方面的理论途径和计算方法。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；监管机构也使用这些办法和方法，以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，我们专门使用由隐马尔可夫模型(HMM)调制的合适的随机过程。在过去的授权期内，我们对隐马尔可夫模型提出了一种统一主题的方法，在这种方法中，人们能够完全在线生成模型参数，甚至能够通过高阶隐马尔可夫模型(HOHMM)利用先前时间滞后的信息。在接下来的五年里，我们将通过优先考虑监管、商业和环境方面的一些当代问题所推动的理论发展和应用，将HMM提升到实用、可获得性和多功能性的新水平。我们将特别审议两个问题主题：(1)设计涵盖(A)金融危机预警系统和(B)网络安全-风险检测工具的预测性分析；(2)对最近的金融创新进行估值，重点是(A)具有投资担保的保险产品和(B)应用于为气候变化适应和灾害风险管理提供资金的天气衍生品。在主题(1)中，我们将为HOHMM控制的Ornstein-Uhlenbeck过程和Bessel过程创建各种扩展的多元滤波算法来捕捉金融压力指数，并对时间序列数据中结构变化的变化点提供在线估计。我们将采用过滤市场方法来处理主题(2)，根据该方法，生成的基于隐马尔可夫模型的参数估计将与构建适当的风险中性措施一起用于为具有复杂功能和回报结构的合同定价。拟议研究的具体成果将包括金融工具估值和对冲的有效计算方法，用于动态参数估计的新的和改进的过滤算法，以及使用HOHMM和信息融合的组合力量对当前紧迫的社会关切的量化解决方案。这项研究将通过培训高素质人员提供技术和实用专门知识，并为跨学科和多学科边界的协同合作开辟更多途径。

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.