Modern statistical methodologies in mortality forecasting and insurance applications

This thesis is a collection of three studies contributing to statistical techniques in mortality forecasting and actuarial applications. Other than oft-explored choices, such as the Clayton, Gumbel-Hougaard and Frank copulas, the first study explores an extensive list of Archimedean copulas for use in general and life insurance modelling. In the empirical data analysis, we first explore the processes of modelling bivariate claims in general insurance based on two general insurance datasets. Then we select appropriate copulas for modelling the mortality trends of three pairs of neighbouring countries and calculate the market price of a mortality bond. Finally, a large simulation exercise investigates further limitations in copula selection. The second study discusses the development and application of methods for calculating health adjusted life expectancy (HALE) for Australian retirement village (RV) residents. With the increase in life expectancy around the world, the demand for and supply of RVs are constantly growing. However, RV contracts are very complicated and effectively involve residents paying rent for their remaining healthy lifespans at the time of entry. Therefore, residents' HALE is a critical factor when considering the value of the accommodation service received. In this study, we develop the Conditional Health Adjusted Life Expectancy (CHALE) and health adjusted survival function for RV residents. We also assess a range of applications and methods to quantify the risks and benefits of RV contracts for residents. Forecasting mortality rates using a two-step LASSO-based vector-autoregressive (2-LVAR) model is the third study of this thesis. As part of the VAR framework, our proposed 2-LVAR model combines the merits of the spatial-temporal VAR (STAR) model and the sparse VAR (SVAR) model and extends the idea of the smoothed SVAR (SSVAR) model. The 2-LVAR model uses undifferentiated mortality rates with non-zero coefficients to ensure age coherence in the forecast mortality rates. We develop a two-step estimation strategy to resolve the challenging objective function of 2-LVAR, which consists of L1 (LASSO-type) and nonstandard L2 penalties with constraints. The empirical evidence of the total mortality rates of four countries demonstrates the effectiveness of our proposed 2-LVAR model in contrast to the Lee-Carter, STAR and SVAR models. Simulation studies confirm this out-performance, and long-term analyses based on life expectancy at birth empirically support the existence of age coherence.