Hidden Markov models for decision analytics

金融数学家工作中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。这些方法和方法被研究人员和从业人员用于投资交易和金融产品/服务创新；监管机构也利用它们来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，我们专门研究使用由隐马尔可夫模型（hmm）调制的合适的随机过程。在之前的授权期间，我们提出了一种统一主题的hmm方法，其中可以完全在线生成模型参数，甚至可以通过高阶hmm （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在监管、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的实用性、可及性和多功能性提升到一个新的水平。特别是，我们将考虑两个问题主题：(1)设计预测分析，涵盖(a)金融危机预警系统和(b)网络安全风险检测工具；(2)对最近的金融创新进行评估，重点关注(a)具有投资担保的保险产品和(b)用于资助气候变化适应和灾害风险管理的天气衍生品。在主题(1)中，我们将针对HOHMM控制下的Ornstein-Uhlenbeck和Bessel过程创建各种扩展的多元滤波算法来捕获金融压力指标，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)，由此生成的基于hmm的参数估计将与具有复杂特征和支付结构的定价合同的适当风险中性措施的构建一起使用。拟议研究的实际成果将包括金融工具估值和套期保值的有效计算方法，用于动态参数估计的新的和改进的过滤算法，以及使用hohmm和信息融合的联合力量对当前紧迫的社会问题的定量解决方案。这项研究将通过培训高素质人才贡献技术和实践专业知识，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.