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Actuarial and Financial Mathematics

Adaptive Monte Carlo Methods for Stochastic Differential Equations

Reference Number: 2018-HW-AMS-14

Abstract: Capturing rare events is crucial for accurate risk assessment and its successful management. An example in finance is computing the probability of a large, but rare, loss from a financial portfolio. Approximating expectations involving such rare events is difficult because, when using Monte Carlo, many of the generated samples do not contribute to the final outcome and the expensive samples are effectively wasted. Adaptive sampling methods resolve this issue by spending some minimal computational effort to determine if a sample is of interest and, only if it is, the sample accuracy is then improved by spending further computational effort.  Using concepts from stochastic analysis, probably theory and numerical analysis, this project will look at applying adaptive methods to compute outputs depending on stochastic differential equations rather than simple random variables.

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Dynamic Futures Contract Modelling and Term Structures

Reference Number: 2018-HW-AMS-11

Abstract: In this project you will explore development multi-factor financial models for commodity futures term structures. It will require developing pricing and state space model regression calibration methods to study dynamics of futures curves with regard to a range of endogenous and exogenous physical and financial variables. This will then work as input to development of convexity trading models for cross curve model based trading strategy. It will be compared to functional data analysis and functional regression methodologies for such futures trading contexts.

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Green finance and Green Bond Modelling

Reference Number: 2018-HW-AMS-09

Abstract: In this project you will explore the development of the green finance industry, with particular focus on green bonds. The selected sub-projects include primary market and secondary market modelling of green bond issuance, pricing, spread models and securitisation. In addition, the firm valuation modelling with regard to ESG, CSR and green bond issuance will be explored and modelled. There is also scope for development of natural language processing methodologies from machine learning to explore the processing of information from green bond second opinion letters and debentures of issuance documents.

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High Frequency Financial Trading and Limit Order Book Modelling

Reference Number: 2018-HW-AMS-10

Abstract: In this project you will explore development of marked Hawkes process models for intra day high frequency finance. It will involve calibration of such models to Limit order book data for equities and futures contracts. This will involve exploring different aspects of estimation and simulation of these self exciting marked point process models. Once such models are developed, this will provide a means to simulate limit order book dynamics that can be used to test trading strategy designs and explore optimal execution in trade placement.

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Machine learning methods for Risk and Insurance

Reference Number: 2018-HW-AMS-08

In this project you will explore a series of machine learning methodological developments to facilitate new approaches to insurance product design and pricing. It will be focused on methodological developments that can be applied to a variety of insurance domains. The work will be primarily exploring aspects of kernel machines, boosting and ensemble methods, random forests, Gaussian processes and warped Gaussian processes to enhance data analytics in insurance applications. The considered application domains will be based on real world problems from both general and life insurance applications.

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Numerical Methods for Financial Market Models

Reference Number: 2018-HW-AMS-01

Abstract: Many existing models for the evolution of financial and economic variables such as interest rates, inflation and so forth have no known closed-form solution. In order to deal with such models, e.g. for pricing and risk management of financial derivatives, it is therefore of fundamental importance to design numerical methods that are highly accurate, fast and robust. This project will apply methods from stochastic analysis and probability theory to models of financial markets to enhance the understanding of their stochastic properties, and to design high-quality fast methods for their numerical treatment.

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Portfolio Design and Feature Extraction Methods in Fiat and Crypto Currency Portfolios

Reference Number: 2018-HW-AMS-13

Abstract: In this project you will explore development of multi-period optimal portfolio design and allocation methods for a range of currency markets both fiat and crypto currency markets. This will involve study of equal risk parity methods as compared to classical global minimum variance and mean-variance methods. It will require analysis of volatility dynamics for returns on currency baskets and the study of effectiveness of carry strategies across a basket of joint fiat and crypto currencies.

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Quantitative Methods and Models with Applications in Finance and Actuarial Science: Valuation Techniques, Investment Strategies and Dependence Modeling

Reference Number: 2018-HW-AMS-15

Various stakeholders in finance and insurance—such as regulators, investors and managers—rely on quantitative analysis in their decision-making processes. This research project employs quantitative models and methods from probability theory and statistics to tackle problems that are of practical relevance in these fields. Three topics are mainly concerned.  The first topic studies numerical techniques that are useful in financial and actuarial valuation such as option pricing, capital allocation and risk aggregation etc. We aim to propose new efficient computational methods and techniques. The second topic studies investment strategies and behaviors under general risk preference with emphasis on portfolio selection, skewness preference and performance measure etc. The third topic delves into dependence modeling of risks and its applications in finance and insurance. It covers popular research questions such as model uncertainty, systemic risk, high-dimensional risk measure and worst-scenario analysis etc.

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Spatial-Temporal Demographic Modelling: Morbidity, Mortality, Annuities and Weather Related Insurance

Reference Number: 2018-HW-AMS-12

Abstract: In this project you will explore development of spatial temporal processes which combine time series methods with machine learning techniques such as warped Gaussian processes and Tukey G-and-H processes as well as multiple hierarchical credibility methods to explore spatial-temporal risk models. This can be used to study aspects of weather related (heatwave etc.) morbidity and mortality events and the influence this could have on annuity portfolios. It will also be useful to study aspects of farming and agricultural insurance. The other aspect of this project that can be explored includes modelling of variable rate annuities.

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• Predictive models in health and morbidity trends related to insurance

Reference Number: 2018-HW-AMS-18

Abstract: Over recent decades, medical interventions and advances have become important drivers of health and morbidity trends. In this project we will consider statistical predictive models for such trends, relating to particular major conditions such as heart disease and cancer. The principal aim will be to address the timely need to develop robust predictive models for rapidly changing morbidity risks and relevant impact on health-related insurance, such as long-term care, disability and critical illness insurance. Bayesian model diagnostics, assessment and selection will be considered for a range of models including machine learning-based approaches.

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• Predictive performance modelling for financial investment strategies

Reference Number: 2018-HW-AMS-16

Abstract: The development of multi-asset quantitative strategies is crucial in the investment industry and requires the analysis of vast amounts of data to gain insight about performance. This project will investigate the use of statistical predictive models and performance measures for risk evaluation in financial investment strategies, aiming to provide increased levels of predictive robustness in modelling under different scenarios. Methodology related to back-testing and statistical machine learning will be used, and model uncertainty will be accounted for under a Bayesian approach.

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