Home | English | | | UGC | RGC
An International Hub for Academic Research
Analyses of Insurance Risk Models with Dividend Payments
Actuarial Science and Finance Model with Dependent Risks
Novel Molecular Mechanisms of innate host defense - Implications on periodontal health and disease
Avian flu nucleoprotein - from basic research to drug development
Effectiveness of Specialized Ventilation Systems in Hospitals of Hong Kong
Complex Network Models of Disease Propagation: Modelling, Predicting and Assessing the Transmission of SARS
RGC Collaborative Research fund - Layman Summaries of Projects Funded in 2008/2009 Exercise


How to measure and manage insurance and finance risks is a practically important and theoretically interesting problem. This project studies some actuarial and finance models with dependent risks. Our main focus is on a popular risk measure in actuarial science: ruin probability. Ruin probability refers to the probability of a company going to bankruptcy. It is well-known that when the model includes dependent structure, the problem becomes very difficult.

We modeled the premium and claims using models which depend on historical information. Markov processes and time series have been used to model the dependent structure. In order to use information of both claim and premium series to predict the future value of one series, we proposed to model this by using Granger's causal model. That model includes the possibility of having causality between premium and claim processes in Granger's sense. The method we used is martingale which is a very powerful mathematical tool. Another class of dependent insurance risk models we have investigated is the threshold insurance risk model. We assume that the claim size of an insurance business depends on the claim time and the solution is to solve the delayed integro-differential equations satisfied by the ruin probability.

By using martingale arguments, we obtained the upper bounds for the ruin probability. The upper bound for the ruin probability can serve as a conservative   estimation   of   the   ruin probability. By solving the delayed integro-differential equations satisfied by the ruin probability, Lundberg type upper bound for the ruin probability has been obtained. We have also inves-tigated the insurance risk models with investment income; both the ruin probability and the absolute ruin probability have been studied. By solving certain type of integro-differential equations, we have obtained closed form solutions for the ruin probability and the absolute ruin probability in the case of claim size following certain class of distributions.

We considered the problem of optimal portfolio selection in multi-period setup with dependent structure where the dependent structure is modeled by a Markov chain. By using the mean-variance approach, we obtained the efficient frontier portfolio and some interesting properties of the optimal strategy. We have proposed using methods and tools in stochastic order theory to study the properties of optimal portfolio strategies. To the best of our knowledge, we are the first to introduce stochastic order tools in portfolio selection research.

Our research work on this project has made significant contribution to the actuarial science literature, provided insights to some important actuarial and finance problems. This project can be considered as research works on the inter play between actuarial science and finance.

Professor Hailiang Yang
Department of Statistics and Actuarial Science
The University of Hong Kong