Applications of time-series models to ruin theory with dependent classes of business

Abstract

Time series analysis has been a prominent research topic in statistics in the past decades. The flexibility and applicability of the subject makes it valuable in a number of broad fields ranging from economics to social sciences. In this talk, we will discuss several time series applications in actuarial science, namely the time series risk model. In traditional ruin theory, a renewal process is considered to capture the effect of premium income and insurance claim expense to the insurer's surplus level. A relatively simple but unrealistic of assumption is to regard distributions among claim size and that among claim numbers as independent. This certainly underestimate the risk of a business in practice, since it is natural that claims with different business classes are correlated. Even for claims in the same book, dependence exists across different time periods. Thus, multivariate time series is certainly a proper tool in modeling the risk structure. In this talk, some time series models in the literature are reviewed. This includes a vector autoregressive (VAR) model with the inclusion of interest. Finite-time and infinite-time ruin probability are also illustrated with the extension to the vector autoregressive moving average (VARMA) model. Further possible applications of other time series models are also discussed to suit various needs in practice, for instance, the use of integer-valued time-series in the number of claims.