Actuarial Science: Theory and Methodology by Hanji Shang PDF

By Hanji Shang

ISBN-10: 7040192322

ISBN-13: 9787040192322

Given that actuarial schooling was once brought into China within the Eighties, chinese language students have paid higher realization to the theoretical study of actuarial technological know-how. Professors and specialists from famous universities in China lately labored jointly at the undertaking "Insurance info Processing and Actuarial arithmetic conception and Methodology," which used to be supported via the chinese language govt. Summarizing what they accomplished, this quantity offers a research of a few easy difficulties of actuarial technology, together with chance versions, danger evaluate and research, and top rate rules. The contributions hide a few new functions of likelihood and facts, fuzzy arithmetic and fiscal economics to the sphere of actuarial practices. Discussions at the new assurance marketplace in China also are provided.

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The methods to determine the coefficients of the decomposition are also given. 2 Actuarial Science: Theory and Methodology Individual Risk Model and Compound Risk Model For a portfolio of policies, let N denote the number of claims during a fixed time period and X\, X2, • • • denote the amounts of successive claims. The total loss of the portfolio during the period can be expressed as N S = J2Xi- (2-1) Here N is a random variable. This model is called compound risk model. When N is a Poisson random variable, it is called compound Poisson model and S is called compound Poisson random variable; When AT is a Binomial random variable, S is called compound Binomial random variable.

Y} V where I{u^y} is the indicator function. 4 Lundberg Bound Following the arguments in [Sundt and Teugels (1995)], we are also able to obtain the Lundberg type inequality. Same as in [Sundt and Teugels (1995)], we assume that (f>(s) has — a as an abscissa of convergence. So for Chapter 1 Risk Models and Ruin 21 Theory any u > 0 and for s G / := (—a, 0), we have /•+oo e-sxdA5{x,y)^e-su{l-As(u,y)}, 7*1 ( * , y ) ^ / Ju so we obtain the Chernoff type estimate 1 - As(u,y) < e x p j mf {sM + log7ai(s, y)}}- (1-38) Let ss(u, y) denote the solution of the following equation: uisi(s,y) = -l'Si(s,y) , (1-39) a=Ufe£Mzf), (L40) and we call \ss(u,y)\ the adjustment function.

2004). On the distribution of surplus immediately after ruin unde interest force and subexponential claims, Insurance: Mathematics and Economics, 35, 703-714. Wang R M, Liu H F. (2002). On the ruin probability under a class of risk processes, Astin Bulletin, 32, 81-90. Willmot G E, Lin X S. (1998). Exact and approximate properties of the distribution of surplus before and after ruin, Insurance: Mathematics and Economics, 23, 91-110. Willmot G E, Lin X S. (2001). Lundberg Approximations for Compound Distributions with Insurance Applications, Lecture Notes in Statistics, 156, New York: Springer-Verlag.

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Actuarial Science: Theory and Methodology by Hanji Shang


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