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By Hanji Shang

For the reason that actuarial schooling was once brought into China within the Nineteen Eighties, chinese language students have paid higher recognition to the theoretical examine of actuarial technology. Professors and specialists from recognized universities in China lately labored jointly at the undertaking "Insurance info Processing and Actuarial arithmetic conception and Methodology," which was once supported through the chinese language executive. Summarizing what they completed, this quantity presents a research of a few uncomplicated difficulties of actuarial technological know-how, together with probability versions, danger evaluate and research, and top class rules. The contributions conceal a few new functions of likelihood and facts, fuzzy arithmetic and monetary economics to the sector of actuarial practices. Discussions at the new assurance marketplace in China also are provided.

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The third section concentrates on the recursive equations of the compound poisson model. First, the one-dimensional recursive equations on mixed type severity distribution is derived (Yang, Cheng and Wu (2005)). Secondly, we present bivariate recursive methods by focusing on excess-ofloss reinsurance (Yang, Cheng and Wang(2004)) . The fourth section presents a new idea to approximate the individual risk models (Yang, Zhou and Zhang (2005)). The total loss of the individual risk models is approximated by a compound Poisson random variable.

2. 42) and the definition of ks(u,y) it follows that Gs{u,y) = l-Es{u,y) = Es(oo,y)-Es{u,y)= Gs(0,y) ldkg(v,y) kg(u,y) -dv v dv u Ju dEs{v,y) dv dv / Ju f k -^dv. 64) Ju Evidently, k*(z,y) ^ ks(z,y) < k*(z,y), it is easy to verify that k*{u,y) f°° k*(v,y)^. k*{i Ju V-* . Gs{u,y) k*{u,y) M)_ r dV ^Gs(0,y)^ u Ju M t ^ A , . (u,y) < Gs(u,y) < G*(u,y). 66) Next, we are going to estimate G*(u,y) and G*(u,y), the lower and upper bounds of Gg(u,y). 8. 1 Suppose that fi(u) ~ gi(u) and fe(u) ~ g2(u),u —> oo.

Then ip(u) = J^K e x P { ~ I+A EM)}> where A = 1 ^ - l = f - l . Before we give the proof of this Corollary, we need the following Lemma, whose proof is very easy by induction, and so is omitted. 2 When 0 < x ^ \, for any nonnegative integer n, the following equality always holds: V(n + 2fc)! 10 interger n, ( ' When 0

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