Mathematical Optimization of Catastrophic Risk Processes via Expectation-Maximization(EM) Algorithms

  • Marian Chatoro

Student thesis: Doctoral ThesisDoctor of Philosophy

Abstract

Recent climate observations and trends dictate multiple possibilities of future overall climate depending on the actions taken in the present. Some views can be optimistic,believing that human beings will soon make the necessary changes required for continued survival, while others are more pessimistic, believing that there is not much that can be done, and that life will end altogether on the planet as Earth slowly converts into a hot and barren wasteland. The answers are rarely clear-cut, but given the ability of human beings to research and understand the driving factors behind such processes,the possibility of optimising our climate conditions for all of earth’s inhabitants is always an option. It is for this reason that there are many who try to improve these conditions as best as they can, even if they are unsure if their efforts produce any tangible long-term results. To optimise our climate processes therefore, it has become important focus on long-term sustainability and renewal of optimal environments, and improvement of disaster risk resilience, especially for the more immediate climate risks.This study intends to contribute to this long-term climate management, by first analysing the history, developments, and trends underlying climate processes, modelling these processes mathematically for the sake of comprehensiveness, and finally applying said models to not only improve climate-based catastrophic risk loss modelling, but also to price and analyse extreme disaster risk financing instruments.In this manner, the study ensures a fuller view of climate processes and their interactions, generates more efficient catastrophic loss models, and improves model applicability to incorporate newer trends in climate change and climate risk financing,while ensuring better model efficiency in terms of both computational performance and tractability. In this manner, the study thus contributes to the very important need for better disaster resilience among communities and societies, a key goal of recent climate agreements, including the Sendai Framework for Disaster Risk Management(SFDRR). The results established here are useful for both practitioners, academics,ivand development-based organisations handling issues of climate and disaster risk, disaster financing, and applied mathematics. In addition, any individual interested in climate impact, mitigation and adaptation can derive value from other elements of the study beyond just its results, including the historical and geological connections that have been discussed.To this effect, therefore, the study focuses on the application of mathematical optimisation, with the Expectation-Maximisation (EM) algorithm in particular, to improve climate-based catastrophic loss modelling and pricing of catastrophic disaster risk financing instruments, and the catastrophe bond in particular. Three main studies are conducted, with the first aiming to assess the catastrophe bond market’s efficiency by analysing the ‘fairness’ of its issuer-specific prices through multi-level random effects modelling, the second to provide a better mathematical optimisation model for the heavy-tailed nature of catastrophic losses through finite mixture modelling, while the third and final study proposes a model that better incorporates dependence single peril dependence structure in observed catastrophic losses by applying hidden Markov models. Apart from these three main studies, historical timelines and developments in climate and financial disaster risk management are also extensively discussed in the remaining sections
Date of AwardMar 2024
Original languageEnglish
Awarding Institution
  • Coventry University
SupervisorPanagiotis Andrikopoulos (Supervisor) & Jia Shao (Supervisor)

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