Grant: Discovery Grants Program - Individual

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.