Topics on Actuarial Applications of Non-Linear Time Series Models

This dissertation, "Topics on Actuarial Applications of Non-linear Time Series Models" by Yin-ting, Chan, 陳燕婷, was obtained from The University of Hong Kong (Pokfulam, Hong Kong) and is being sold pursuant to Creative Commons: Attribution 3.0 Hong Kong License. The content of this dissertation has not been altered in any way. We have altered the formatting in order to facilitate the ease of printing and reading of the dissertation. All rights not granted by the above license are retained by the author. Abstract: Abstract of the thesis entitled TOPICS ON ACTUARIAL APPLICATIONS OF NON-LINEAR TIME SERIES MODELS submitted by Chan Yin Ting for the degree of Master of Philosophy at The University of Hong Kong in July 2005 In actuarial science, stochastic models have wide applications in mod- elling survivals, equity returns, and interest rates. This study examines actuarial applications of time series modelling and exaimnes related theo- retical issues. In the insurance market, investment guarantees are popular. Managing the risks of investment guarantees is thus important. Recent researcher in Canada and the United States have spent much efforts on this topic. This study adds to this research area by investigating the use of time series models in managing the risks of investment guarantees in Hong Kong. Since the Office of the Commissioner of Insurance in Hong Kong re- quires the reserving standards for investment guarantees in Hong Kong be based on stochastic analysis, this study contributes to this research area by proposing a favourable time series model for Hong Kong equity returns. The results show that the two-state Markov switching Gaussian model is favourable. To make sure that the tail behaviour of models used in the stochastic analysis are reasonable, we establish a calibration test for investment guarantees in Hong Kong. Finally, reserving standards for investment guarantees in Hong Kong are studied through a simple illus- tration, and the results show that reserving standards in Hong Kong aremuch higher than in Canada and the United States. The results highlight the volatility of the Hong Kong stock market and the risks associated with investment guarantees for insurers in Hong Kong. Investment guarantees are products of long holding periods, such as five years or ten years. Although we are interested in the long-term equity returns, we often use data of higher frequency, such as monthly data, since data of low frequency are often too sparse for good model fitting. This practice leads us to study a theoretical issue, which is the relationship between data of high frequency and data of low frequency. In the statistical literature, this issue belongs to the study of temporal aggregation of time series models. Temporal aggregation for linear time series has been widely studied. In this study, we extend the results to three classes of non-linear time se- ries models, namely, the Markov switching Gaussian models, the mixed auto-regressive model, and the bilinear model. Closed form formulas are obtained for the mean, variance, and autocovariances of the temporally aggregated models. The results and techniques of our study are then used to perform a comparative study of data disaggregation methods, and to examine the illusory long memory effect of the Markov switching Gaussian models. The results provide useful information on the performance of var- ious data disaggregation methods for non-linear time series models. Also, the results show the potential of temporal aggregation for distinguishing long memory from regime switching. DOI: 10.5353/th_b3200209 Subjects: Time-series analysis Investments - Mathematical models