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精算学——理论与方法(英文版)
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精算学——理论与方法(英文版)

  • 作者:尚汉冀(Shang Hanji)
  • 出版社:高等教育出版社
  • ISBN:9787040192322
  • 出版日期:2006年04月01日
  • 页数:266
  • 定价:¥58.00
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    内容提要
    Since actuarial educ ation was introduced into China in 1980s, more and more attention have been paid to the theoretical and practical research of actuarial science in China.
    In 1998, the National Natural Science Foundation of China approved a 1 million Yuan RMB financial support to a key project 《Insurance Information Processing and Actuarial Mathematics Theory & Methodology》(project 19831020), which is the first key project on actuarial science supported by the government of China. From 1999
    目录
    Preface
    Chapter 1 Risk Models and Ruin Theory
    1.1 On the Distribution of Surplus Immediately after Ruin under Interest Force
    1.1.1 The Risk Model
    1.1.2 Equations for G (u, y)
    1.1.2.1 Integral Equations for (u, y), G(u, y) and G(u, y)
    1.1.2.2 The Case
    1.1.3 Upper and Lower Bounds for G(0, y)
    1.2 On the Distribution of Surplus Immediately before Ruin under Interest Force
    1.2.1 Equations for B(u,y)
    1.2.1.1 Integral Equations for B(u,y)
    1.2.1.2 The Case=0
    1.2.1.3 Solution of the Integral Equation
    1.2.2 B(u,y) with Zero Initial Reserve
    1.2.3 Exponential Claim Size
    1.2.4 Lundberg Bound
    1.3 Asymptotic Estimates of the Low and Upper Bounds for the
    Distribution of the Surplus Immediately after Ruin under
    Subexponential Claims
    1.3.1 Preliminaries and Auxiliary Relations
    1.3.2 Asymptotic Estimates of the Low and Upper Bounds
    1.4 On the Ruin Probability under a Class of Risk Processes
    1.4.1 The Risk Model
    1.4.2 The Laplace Transform of the Ruin Probability with Finite Time
    1.4.3 Two Corollaries
    Chapter 2 Compound Risk Models and Copula De-composition
    2.1 Introduction
    2.2 Individual Risk Model and Compound Risk Model
    2.2.1 The Link between the Compound Risk Model and the Individual Risk Model
    2.2.2 One Theorem on Excess-of-loss Reinsurance
    2.3 Recursive Calculation of Compound Distributions
    2.3.1 One-dimensional Recursive Equations
    2.3.2 Proofs of Theorems 2.2-2.3
    2.3.3 Bivariate Recursive Equations
    2.4 The Compound Poisson Random Variable's Approximation to the Individual Risk Model
    2.4.1 The Existence of the Optimal Poisson r.v
    2.4.2 The Joint Distribution of (N(0), N)
    2.4.3 Evaluating the Approximation Error
    2.4.4 The Approximation to Functions of the Total Loss
    2.4.5 The Uniqueness of the Poisson Parameter to Minimiz-ing Hn (0)
    2.4.6 Proofs
    2.5 Bivariate Copula Decomposition
    2.5.1 Copula Decomposition
    2.5.2 Application of the Copula Decomposition
    Chapter 3 Comonotonically Additive Premium Principles and Some Related Topics
    3.1 Introduction
    3.2 Characterization of Distortion Premium Principles
    3.2.1 Preliminaries
    3.2.2 Greco Theorem
    3.2.3 Characterization of Distortion Premium Principles
    3.2.4 Further Remarks on Additivity of Premium Principles
    ……

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