Dependent And Heterogeneous Risk Premium Calculated

The subject of risk management has been most concerned in the financial fields including banking, securities bussiness, insurance, etc., since 1990s. The techniques of risk management have developed rapidly, such as the method of value-at-risk, stochastic orders and copulas. Stochastic orders and copulas are both effective tools for dealing with the problems about risk portfolios. Stochastic orders are usually helpful in the comparison of individual risks, see [M(u|¨)ller and Stoyan(2002)] for detail. A copula which is a function that links univariate margins to the multivariate distribution perfectly describes the dependent stucture among multivariate random variables, see [Nelsen(1999)] for detail.In the thesis, we analysis the effects of dependent and heterogeneous individual risks on the premiums of life-insurance policies portfolios and multi-life status policies using stochastic orders and copulas. It consists of three chapters.In chapter one, we present the definitions and properties of some tools used in the sequel.In chapter two, we focuse on discussion on life-insurance policies portfolios. Firstly, in section one, we derive the strong limiting of the average benefit present value function of a homogeneous portfolio composed by m whole life insurance policies with the independence assumption among the future-lifetime random variables of the insured under the stochastic interest rate. Moreover, we obtain the upper and lower convex bounds of the strong limiting. Secondly, in section two, we apply the results obtained in [Dahan et al.(2003,2004)] to discuss the effects of heterogeneity (life-distribution, the age at issue time) among the insured on the periodical premiums of two different endowment policies portfolios.In chapter three, we investigate the effects of dependencies and heterogeneity among the single lives on the premiums of multi-life status policies using stochastic orders and copulas. Firstly, in section one, we apply some advanced techniques in dealing with multivariate dependent risks to generalize some important results of [Denuit and Dhaene et al.(2001)] for the bivariate cases to the multivariate cases. secondly, in section two, we take two classes of endowment contracts into accout. We apply Majorization order, Schur functions, α—PAs fractional age assumption and some related results of [Dahan et al. (2003,2004)] to study the effects of heterogeneity among the single lives on the periodical premiums of joint-life and last-survivor statuses endowment contracts. We model the dependent structure among the...