Electronic Thesis and Dissertation Repository

Degree

Doctor of Philosophy

Program

Statistics and Actuarial Sciences

Supervisor

Dr. Rogemar Mamon; Dr. Xiaoming Liu

Abstract

This thesis develops stochastic modelling frameworks for the accurate pricing and risk management of complex insurance products with option-embedded features. We propose stochastic models for the evolution of the two main risk factors, the interest rate and mortality rate, which could also have a correlation structure. For the valuation problem, a general framework is put forward where correlated interest and mortality rates are modelled as affine-diffusion processes. A new concept of endowment-risk-adjusted measure is introduced to facilitate the calculation of the GAO value. As a natural offshoot of addressing GAO valuation, we derive the convex-order upper and lower bounds of GAO values by employing the comonotonicity theory.

As an alternative to affine structure, we construct a more flexible modelling framework that incorporate regime-switching dynamics of interest and mortality rates governed by a continuous-time Markov chain. The corresponding endowment-risk-adjusted measures are constructed and employed to obtain more efficient GAO pricing formulae. An extension of the previous modelling set-up is further developed by integrating the affine structure and regime-switching feature. Both interest and mortality risk factors follow correlated affine structure whilst their volatilities are modulated by a Markov chain process. The change of probability measure technique is again utilised to generate pricing expressions capable of significantly cutting down computing times.

Finally, the risk management aspect of GAO is investigated by evaluating various risk measurement metrics. The bootstrap technique is used to quantify standard error for the estimates of risk measures under a stochastic modelling framework in which death is the only decrement.


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