What Is Risk Theory?

This book is a revision of the first chapter "Loss Distribution" and the second part "Risk Theory" of the Chinese actuary qualification exam book "Risk Theory and Non-Life Insurance Actuarial". Risk theory. ^[1]

Risk theory

Risk is the foundation of insurance. It should be said that from the moment insurance was born, people began to consciously control certain risks in the objective world effectively, and they began to analyze and research risks consciously or unconsciously. However, the systematic and effective quantitative research on risk in the true sense is still after the Department of Probability and Statistics. Probability and statistics are subjects that study uncertainty or randomness. Insurance risk theory uses probability and statistics as a research tool to quantitatively characterize the loss risk and operating risk of insurance operations, establish models and study the nature of models, and provide technical support for effective risk analysis and control in realistic insurance operations. .

The book is divided into two parts and a total of eight chapters. Its contents mainly include risk theory and insurance actuarial, Bayesian method of loss distribution, uniformly distributed random numbers and pseudo-random numbers, insurance risk models, long-term aggregate risk models, and bankruptcy theory.

Chapter 1: Risk Theory and Actuarial Insurance

1.1 The concept of risk

1.2 Risk Theory and Insurance Actuarial

1.3 The main content of this book

The first part of the loss distribution

Chapter II Loss Distribution

2.1 Introduction

2.2 Probabilistic basis of loss distribution analysis

2.3 Fitting the loss distribution

Chapter 3 Bayesian method of loss distribution

3.1 Introduction

3.2 Prior Probability

3.3 posterior probability

3.4 Bayesian estimation

3.5 Subjective probability

Chapter 4 Stochastic Simulation

4.1 Introduction

4.2 Uniformly distributed random numbers and pseudo-random numbers

4.3 Random Numbers in General Distribution

4.4 Simulation application examples

4.5 Volume of simulation samples

Attached: Uniformly distributed random number table on [0,1]

Part II Insurance Risk Model

Chapter 5 Short-term Individual Risk Model

5.1 Introduction

5.2 Claim distribution of individual policies

5.3 Independent and Distributed Convolutions

5.4 Moment generating function method to calculate claims distribution

5.5 Normal distribution approximation of the Prime Minister's compensation model

Chapter 6 Short-Term Aggregation Risk Model

6.1 Introduction

6.2 Number of claims and distribution of claims

6.3 Total claims model

6.4 Compound Poisson Model

6.5 Approximate Model

Chapter VII Long-Term Aggregation Risk Model and Bankruptcy Theory

7.1 Earnings Process and Bankruptcy Probability

7.2 Premier compensation process

7.3 Ruin probability

7.4 Ruin probability and adjustment coefficient

7.5 Discrete model

7.6 Application of Bankruptcy Theory

Chapter VIII Utility Theory and Insurance Decision

8.1 Introduction

8.2 Expected Utility Principle

8.3 Risk attitude

8.4 Premium design principles

8.5 Optimal insurance

appendix

Appendix I Common Probability Distributions and Their Properties

Appendix II: Solutions to Exercises

references