On insurance risk models with correlated classes of business

On insurance risk models with correlated classes of business

吳學淖(Xueyuan Wu)

香港大學/Doctor of Philosophy/Statistics and Actuarial Science/博士(2004年)

並列摘要

(Uncorrected OCR)
Abstract of the thesis entitled

ON INSURANCE RISK MODELS WITH CORRELATED CLASSES OF BUSINESS

submitted by Wu Xueyuan

for the degree of Doctor of Philosophy

at The University of Hong Kong in February 2004

In this thesis, we focus on ruin analysis of risk models wIth correlated classes of insurance business. Specifically, five risk models with different dependence relations between classes are introduced. For these models, various problems related to ruin probability are considered.

vVe first study a continuous-time correlated aggregate clmms model with Poisson and Erlang risk processes. In this model, we assume that two classes of business are correlated through a common Erlang component in thelf claim-number processes. We derive an explicit expression for the mfimte-time survival probability of the assumed model when claim SIzes are exponentially distributed. For general claim-size distributions, we obtain some result for the infinite-time ruin

probabIlIty, and present a numerical method for evaluating the probability of

rum.

Based on the continuous-tIme model of Yuen and ’Vang (2002) with thin-

ning correlatIOn, we propose a new dependence relatIOn with interaction between classes of business in the discrete-time case. Two dIscrete-time risk models with such a relation of dependence are studied. For the first interaction model: we investIgate the statIstical properties of the aggregate claIms for a family of claimnumber distributions. Ve also compare the model with other existing models with correlated aggregate claIms in terms of the finite-time and infimte-time ruin probabllitles. The second model extends the interaction dependence to the case of the compound binomlal model with delayed claims. For this model, we develop a recursive method to compute the finite-time survival probabilities: and derive an explicit expression for the infinite-time survival probability in a special case.

The last two risk models proposed in this thesis are the bivariate compound binomial model and the bivariate compound Poisson model. In the bivariate case: vanous definitions of ruin can be considered. For the bivariate compound binomial model, recursive algorithms for calculating several kinds of finite-time survival probability are presented and numerical examples are given. As for the bivariate compound Poisson model, we study the probabllity that at least one of the two classes of business will get ruined. Since this bivanate ruin probability is very dlfficult to deal with, we use the result of the bivariate compound binomial model to approximate the desired bivanate finite-time survlval probability. Ve also obtain an upper bound for the infinite-time ruin probability via some association properties of the model. For a simplified version of the model, we examine

’l’l

the mfimte-time ruin probability when claIm sizes are exponentially distributed.

並列關鍵字

University of Hong Kong - Dissertations. ； Risk (Insurance) - Statistical methods.