Actuarial Science

The following sections are included:

• Preface

• Contents

The following sections are included:

• On the Distribution of Surplus Immediately after Ruin under Interest Force
  • The Risk Model
  • Equations for
    • Integral Equations for , Ḡ_δ(u, y) and G_δ(u,y)
    • The Case δ = 0
  • Upper and Lower Bounds for Ḡ_δ(0, y)

• On the Distribution of Surplus Immediately before Ruin under Interest Force
  • Equations for B_δ(u, y)
    • Integral Equations for B_δ(u,y)
    • The Case δ = 0
    • Solution of the Integral Equation
  • B_δ(u, y) with Zero Initial Reserve
  • Exponential Claim Size
  • Lundberg Bound

• Asymptotic Estimates of the Low and Upper Bounds for the Distribution of the Surplus Immediately after Ruin under Subexponential Claims
  • Preliminaries and Auxiliary Relations
  • Asymptotic Estimates of the Low and Upper Bounds

• On the Ruin Probability under a Class of Risk Processes
  • The Risk Model
  • The Laplace Transform of the Ruin Probability with Finite Time
  • Two Corollaries

• References

The following sections are included:

• Introduction

• Individual Risk Model and Compound Risk Model
  • The Link between the Compound Risk Model and the Individual Risk Model
  • One Theorem on Excess-of-loss Reinsurance

• Recursive Calculation of Compound Distributions
  • One-dimensional Recursive Equations
  • Proofs of Theorems 2.2-2.3
  • Bivariate Recursive Equations

• The Compound Poisson Random Variable's Approximation to the Individual Risk Model
  • The Existence of the Optimal Poisson r.v
  • The Joint Distribution of (, N_n)
  • Evaluating the Approximation Error
  • The Approximation to Functions of the Total Loss
  • The Uniqueness of the Poisson Parameter to Minimizing H_n(θ)
  • Proofs

• Bivariate Copula Decomposition
  • Copula Decomposition
  • Application of the Copula Decomposition

• References

The following sections are included:

• Introduction

• Characterization of Distortion Premium Principles
  • Preliminaries
  • Greco Theorem
  • Characterization of Distortion Premium Principles
  • Further Remarks on Additivity of Premium Principles
    • Representation of Strictly Additive Premium Principles
    • Relationship among Additivities

• Natural Sets of Distortion Premium Principles

• Ordering Risks by Distortion Premiums
  • n-ordered Orders of Real-valued Random Variables
  • n-ordered Dual Orders of Real-valued Random Variables

• Final Remarks

• References

The following sections are included:

• Introduction

• Fuzzy Comprehensive Evaluation for Risks
  • Basic Concepts and Process
    • Construct Factor Set
    • Construct Weight Set
    • Construct Evaluation Set
    • Single Factor Fuzzy Evaluation
    • Fuzzy Comprehensive Evaluation
  • An Example of Risk Evaluation
    • Determination of Main Risk Factors
    • Evaluation of the Risk
    • Applications

• Fuzzy Information Distribution in Risk Evaluation and Analysis
  • Concept of Fuzzy Information Distribution
  • Information Distribution Method
  • Improving IDM
  • Applications

• Information Diffusion and Its Application to Risk Analysis
  • Mechanism of Information Diffusion
  • An Example of Application — 1D Problem
    • Large Sample
    • Small Sample — Statistical Approach
    • Small Sample — UIDM
  • An Example of Application — 2D Problem
    • Large Sample
    • Small Sample — Statistical Approach
    • Small Sample — UIDM
  • Optimized Information Diffusion Method (OIDM)
    • OIDM in 1D Case
    • OIDM in 2D Case

• Conclusion

• References

The following sections are included:

• Introduction

• Some Basic Notions of Fuzzy Set Theory

• Application of FST in Life Insurance Game
  • Background
  • Some Relative Concepts and Theorems
  • Model of Game
  • The Example of Application
    • The Example
    • Conclusion

• Decision-Making Method Applied in Life Insurance Companies
  • Background
  • The Passive Decision—Two-stage Fuzzy Comprehensive Valuation
  • The Initiative Decision—Multi-object Fuzzy Group Decision
  • Synthetic Decision

• The Risk Analysis of Complications for Some Diseases
  • Background
  • The Risk of Complications
    • Determining the Variable
    • Define the Similar Matrix R
    • The Transitive Closure t(R)
    • Optimum Fuzzy Equivalent Matrix R_min
    • Some Results
  • The Illness Degree of Diseases
    • Basic Concept and Method
    • ξ_h: Illness Degree of Hypertension(IDOH)
    • ξ_c: Illness Degree of Coronary Heart Disease (IDOC)
    • The Relationship between Hypertension and Coronary Heart Disease
    • The Application to Insurance

• Regression Forecasting Model with Fuzzy Factors
  • Background
  • Regression Forecasting Model with Crisp Factors
  • Regression Forecasting Model with Crisp Factors and Fuzzy Factors
    • Some Concepts, Methods and an Application Example
    • Regression Forecasting Model with Crisp Factors and Fuzzy Factors
  • Example and Comparison of Two Kinds of Regression Model
  • Conclusion

• References

The following sections are included:

• Introduction

• General Framework of the Valuation of Unit-linked Insurance Policy
  • Differential Equation Models for the Valuation of Policies without Surrender Option
  • P.D.E. Model for the Valuation of Policies with Surrender Option
  • Generalized Expected Discounted Value Approach

• Fair Valuation of First Kind of Unit-linked Policy
  • The Case σ(t, A) = 0
  • The Case σ(t, A) ≠ 0

• Fair Valuation of Second Kind of Unit-linked Policy without Surrender Option
  • P.D.E. Approach
  • G.E.D.V. Approach

• Fair Valuation of Second Kind of Unit-linked Policy with Surrender Option
  • Analysis of Parameters
  • Local Analysis of Free Boundary near the Expiry Date
  • Integral Equation on ν(t, A)
  • Numerical Results
    • Linear Complementary Problem and Projected SOR Method
    • Solving Integral Equation (6.131)

• References

The following sections are included:

• Introduction

• Toward a Risk-oriented Approach of Solvency Supervision System for China Insurers
  • Internal Control
  • Solvency Capital Requirement
  • On Site Inspection
  • Investment Control
  • Guarantee Fund

• Risk Construction of Chinese Insurers
  • Risk Concepts
  • Identification of Methodologies
    • Normative Studies: International Comparisons and Case Analysis
    • Statistical Analysis
    • Field Study and Cases Analysis on China Insurers
    • Combined Approach
  • Keeping Up an Overall and Historical View on the Evolution of Risk Profile of China Insurance
    • Period 1: 1980 — 1995
    • Period 2: 1995 — End of 2003
    • Period 3: 2004 — Near Future
  • Risk Characteristics and Proposed Principles for Solvency Capital Requirement
    • Main Characteristics of Risk Profile
    • Guiding Principles for Setting Capital Requirement

• References

The following sections are included:

• Index