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34 reviews
ISBN 10: 9812565051
ISBN 13: 9789812565051
Author: Hanji Shang
Since actuarial education was introduced into China in the 1980s, Chinese scholars have paid greater attention to the theoretical research of actuarial science. Professors and industry experts from well-known universities in China recently worked together on the project “Insurance Information Processing and Actuarial Mathematics Theory and Methodology”, which was supported by the Chinese government. Summarizing what they achieved, this volume provides a study of some basic problems of actuarial science, including risk models, risk evaluation and analysis, and premium principles. The contributions cover some new applications of probability and statistics, fuzzy mathematics and financial economics to the field of actuarial practices. Discussions on the new insurance market in China are also presented.
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 Gs (u y)
1.1.2.1 Integral Equations for Gs (u y) Gs (u y) and Gs(u y)
1.1.2.2 The Case S = 0
1.1.3 Upper and Lower Bounds for Gs(0 y)
1.2 On the Distribution of Surplus Immediately before Ruin under Interest Force
1.2.1 Equations for Bs(u y)
1.2.1.1 Integral Equations for Bs(u y)
1.2.1.2 The Case S = 0
1.2.1.3 Solution of the Integral Equation
1.2.2 Bs(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
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 Decomposition
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 T.v
2.4.2 The Joint Distribution of (Non(0)Nn)
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 Minimizing 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
3.2.4.1 Representation of Strictly Additive Premium Principles
3.2.4.2 Relationship among Additivities
3.3 Natural Sets of Distortion Premium Principles
3.4 Ordering Risks by Distortion Premiums
3.4.1 n-ordered Orders of Real-valued Random Variables.
3.4.2 n-ordered Dual Orders of Real-valued Random Variables
3.5 Final Remarks
Chapter 4 Fuzzy Comprehensive Evaluation and Fuzzy Information Processing for Risks
4.1 Introduction
4.2 Fuzzy Comprehensive Evaluation for Risks
4.2.1 Basic Concepts and Process
4.2.1.1 Construct Factor Set
4.2.1.2 Construct Weight Set
4.2.1.3 Construct Evaluation Set
4.2.1.4 Single Factor Fuzzy Evaluation
4.2.1.5 Fuzzy Comprehensive Evaluation
4.2.2 An Example of Risk Evaluation
4.2.2.1 Determination of Main Risk Factors
4.2.2.2 Evaluation of the Risk
4.2.2.3 Applications
4.3 Fuzzy Information Distribution in Risk Evaluation and Analysis
4.3.1 Concept of Fuzzy Information Distribution
4.3.2 Information Distribution Method
4.3.3 Improving IDM
4.3.4 Applications
4.4 Information Diffusion and Its Application to Risk Analysis
4.4.1 Mechanism of Information Diffusion
4.4.2 An Example of Application - ID Problem
4.4.2.1 Large Sample
4.4.2.2 Small Sample - Statistical Approach
4.4.2.3 Small Sample - UIDM
4.4.3 An Example of Application - 2D Problem
4.4.3.1 Large Sample
4.4.3.2 Small Sample - Statistical Approach
4.4.3.3 Small Sample - UIDM
4.4.4 Optimized Information Diffusion Method (OIDM)
4.4.4.1 OIDM in 1D Case
4.4.4.2 OIDM in 2D Case
4.5 Conclusion
Chapter 5 Application of Fuzzy Mathematics to Actuarial Science
5.1 Introduction
5.2 Some Basic Notions of Fuzzy Set Theory
5.3 Application of FST in Life Insurance Game
5.3.1 Background
5.3.2 Some Relative Concepts and Theorems
5.3.3 Model of Game
5.3.4 The Example of Application
5.3.4.1 The Example
5.3.4.2 Conclusion
5.4 Decision-Making Method Applied in Life Insurance Companies
5.4.1 Background
5.4.2 The Passive Decision - Two-stage Fuzzy Comprehensive Valuation
5.4.3 The Initiative Decision - Multi-object Fuzzy Group Decision
5.4.4 Synthetic Decision
5.5 The Risk Analysis of Complications for Some Diseases
5.5.1 Background
5.5.2 The Risk of Complications
5.5.2.1 Determining the Variable
5.5.2.2 Define the Similar Matrix R
5.5.2.3 The Transitive Closure t(R)
5.5.2.4 Optimum Fuzzy Equivalent Matrix Rmin
5.5.2.5 Some Results
5.5.3 The Illness Degree of Diseases
5.5.3.1 Basic Concept and Method
5.5.3.2 Eh: Illness Degree of Hypertension(IDOH)
5.5.3.3 Eh: Illness Degree of Coronary Heart Disease (IDOC)
5.5.3.4 The Relationship between Hypertension and Coronary Heart Disease
5.5.3.5 The Application to Insurance
5.6 Regression Forecasting Model with Fuzzy Factors
5.6.1 Background
5.6.2 Regression Forecasting Model with Crisp Factors
5.6.3 Regression Forecasting Model with Crisp Factors and Fuzzy Factors
5.6.3.1 Some Concepts Methods and an Application Example
5.6.3.2 Regression Forecasting Model with Crisp Factors and Fuzzy Factors
5.6.4 Example and Comparison of Two Kinds of Regression Model
5.6.5 Conclusion
Chapter 6 Some Applications of Financial Economics to Insurance
6.1 Introduction
6.2 General Framework of the Valuation of Unit-linked Insurance Policy
6.2.1 Differential Equation Models for the Valuation of Policies without Surrender Option
6.2.2 P.D.E. Model for the Valuation of Policies with Surrender Option
6.2.3 Generalized Expected Discounted Value Approach
6.3 Fair Valuation of First Kind of Unit-linked Policy
6.3.1 The Case o(t A) = 0
6.3.2 The Case o(t A) # 0
6.4 Fair Valuation of Second Kind of Unit-linked Policy without Surrender Option
6.4.1 P.D.E. Approach
6.4.2 G.E.D.V. Approach
6.5 Fair Valuation of Second Kind of Unit-linked Policy with Surrender Option
6.5.1 Analysis of Parameters
6.5.2 Local Analysis of Free Boundary near the Expiry Date
6.5.3 Integral Equation on v(t A)
6.5.4 Numerical Results
6.5.4.1 Linear Complementary Problem and Projected SOR Method
6.5.4.2 Solving Integral Equation (6.131)
Chapter 7 Exploring on the Risk Profile of China Insurance for Setting Appropriate Solvency Capital
7.1 Introduction
7.2 Toward a Risk-oriented Approach of Solvency Supervision System for China Insurers
7.2.1 Internal Control
7.2.2 Solvency Capital Requirement
7.2.3 On Site Inspection
7.2.4 Investment Control
7.2.5 Guarantee Fund
7.3 Risk Construction of Chinese Insurers
7.3.1 Risk Concepts
7.3.2 Identification of Methodologies
7.3.2.1 Normative Studies: International Comparisons and Case Analysis
7.3.2.2 Statistical Analysis
7.3.2.3 Field Study and Cases Analysis on China Insurers
7.3.2.4 Combined Approach
7.3.3 Keeping Up an Overall and Historical View on the Evolution of Risk Profile of China Insurance
7.3.3.1 Period 1: 1980 - 1995
7.3.3.2 Period 2: 1995 - End of 2003
7.3.3.3 Period 3: 2004 - Near Future
7.3.4 Risk Characteristics and Proposed Principles for Solvency Capital Requirement
7.3.4.1 Main Characteristics of Risk Profile
7.3.4.2 Guiding Principles for Setting Capital Requirement
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Tags: Hanji Shang, Actuarial, Science
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