Physical Sciences and Mathematics Commons^™

Compound Sums, Their Distributions, And Actuarial Pricing, Ang Li

Electronic Thesis and Dissertation Repository

Compound risk models are widely used in insurance companies to mathematically describe their aggregate amount of losses during certain time period. However, evaluation of the distribution of compound random variables and the computation of the relevant risk measures are non-trivial. Therefore, the main purpose of this thesis is to study the bounds and simulation methods for both univariate and multivariate compound distributions. The premium setting principles related to dependent multivariate compound distributions are studied. .

In the first part of this thesis, we consider the upper and lower bounds of the tail of bivariate compound distributions. Our results extend those …

On The Estimation Of Heston-Nandi Garch Using Returns And/Or Options: A Simulation-Based Approach, Xize Ye

Electronic Thesis and Dissertation Repository

In this thesis, the Heston-Nandi GARCH(1,1) (henceforth, HN-GARCH) option pricing model is fitted via 4 maximum likelihood-based estimation and calibration approaches using simulated returns and/or options. The purpose is to examine the benefits of the joint estimation using both returns and options over the fundamental returns-only estimation on GARCH models. From our empirical studies, with the additional option sample, we can improve the efficiency of the estimates for HN-GARCH parameters. Nonetheless, the improvements for the risk premium factor, both from empirical standard errors, and sample RMSEs, are insignificant. In addition, option prices are simulated with a pre-defined noise structure and …

A Class Of Phase-Type Ageing Models And Their Lifetime Distributions, Boquan Cheng

Electronic Thesis and Dissertation Repository

Ageing is a universal and ever-present biological phenomenon. Yet, describing the ageing mechanism in formal mathematical terms — in particular, capturing the ageing pattern and quantifying the ageing rate — has remained a challenging actuarial modelling endeavour. In this thesis, we propose a class of Coxian-type Markovian models. This class enables a quantitative description of the well-known characteristics of ageing, which is a genetically determined, progressive, and essentially irreversible process. The unique structure of our model features the transition rate for the ageing process and a functional form for the relationship between ageing and death with a shape parameter that …

The Mean-Reverting 4/2 Stochastic Volatility Model: Properties And Financial Applications, Zhenxian Gong

Electronic Thesis and Dissertation Repository

Financial markets and instruments are continuously evolving, displaying new and more refined stylized facts. This requires regular reviews and empirical evaluations of advanced models. There is evidence in literature that supports stochastic volatility models over constant volatility models in capturing stylized facts such as "smile" and "skew" presented in implied volatility surfaces. In this thesis, we target commodity and volatility index markets, and develop a novel stochastic volatility model that incorporates mean-reverting property and 4/2 stochastic volatility process. Commodities and volatility indexes have been proved to be mean-reverting, which means their prices tend to revert to their long term mean …