Weighted Risk Capital Allocation Model (WRCAM) And Its Extension On CAPM

With the rapid development in the industry of insurance and the fuse of banking and insurance business, the demand of practicability and rationality in the actuarial pricing principles becomes more and more important for the actuarial professionals. The limitations of traditional premium calculation principles (pcp) become more and more serious (e.g. the independence assumption between risks),therefore, new pcp had been proposed to to meet the needs of the market. e.g. Bulmann's limit theory for posterior distributions (Buhlmann(1980,1984)), Yarri's duality theory (Yarri (1987)),Wang's risk adjustment theory, young's optimal pricing model (young (2000)).This paper is a general review mainly on the model of weighted risk capital allocation proposed by Furman and Zitikis (WRCAM), which dims the individual risk and the overall risk as bivariate random variables. Specifically, consider the poo1{X1,X2...XK},the function of weighted risk capital allocation Hw(X,Y) can be denoted by in which, Y, the overall risk, can, for example, be the linear combination the sum Under this model, different weighted functions matches different pcp. A number of well known allocation rules are special cases of Hw(X,Y)(e.g. the Esscher's functionω(y)=ety, Kamp's (ω(y)=1-e-ty)),therefore this model is can to some extent be regarded as a summary of he previous achievements. Moreover, more and more reasonable distributions,without be applied though, may make an difference.The paper discuss the background, properties, Computational Method and application range. particularly, showed at the end of the paper, the WIPM(weighted insurance pricing model) derived by WRCAM, which is is analogous to the capital asset pricing model (CAPM) in finance (Sharpe (1964), Lintner (1965) and Black (1972)).to be further,this paper gives the comparation between this two models. According to the result, founding that WIPM has a wider application condition than CAPM (only establish with the distribution of bivariate normal), nevertheless, the wide application of CAPM will play an important part on the switch from the traditional insurance products to the financial insurance products. Therefore, the blend of WIPM and CAPM for one part has the function of distribution for the risk compensation, and for the other part,the function of optimizing our profitability to meet the need of investing and financing.