1.     INTRODUCTION

2.     THE NUMBER OF CLAIMS

2.1           The (a,b,0) class of distributions

2.2           Counting processes

2.2.1          Introduction

2.2.2          Homogeneous Poisson process

2.2.3          Non-homogeneous Poisson process

2.2.4          Mixed Poisson process

2.3           The class (a,b,1) of distributions: Truncation and modification at zero

2.4           Model selection: Qui-square test

3.     IMPACT OF COVERAGE MODIFICATIONS IN THE FREQUENCY AND SEVERITY

3.1           Deductible

3.2           Inflation effects

3.3           Policy limits

3.4           Coinsurance, deductibles and limits

3.5           The impact of deductibles on the claim frequency

4.     AGGREGATE LOSS MODELS

4.1           Collective risk model versus individual risk model

4.2           Assumptions and characteristics of the compound model

4.3           Special cases

4.4           The aggregate claim distribution

4.4.1          Introduction

4.4.2          Recursive method

4.4.3          Constructing arithmetic distributions

4.5           The impact of individual policy modifications on the aggregate claim distribution

4.6           The individual model

4.7           Approximated methods

4.7.1          The Normal Power approximation

4.7.2          The translated Gamma approximation

5.     PREMIUM PRINCIPLES

5.1           Some premium calculation principles

5.2           Properties

6.     RISK MEASURES

6.1           Coherent risk measures

6.2           Value at Risk (VaR)

6.3           Tail Value at Risk (TVaR)

6.4           Conditional Tail Expectation (CTE)

6.5           Expected Shortfall (ES)

 

7.     REINSURANCE

7.1           Introduction

7.2           Quota share reinsurance

7.3           Surplus reinsurance

7.4           Excess of loss reinsurance, per risk and per event covers, working and clash covers

7.5           Stop loss reinsurance

8.     RUIN THEORY

8.1           Continuous time model versus discrete time model

8.2           Continuous time model

8.2.1          The adjustment coefficient

8.2.2          Some functional equations for the ultimate probability of ruin

8.2.3          Lundberg's inequality

8.2.4          The maximum aggregate loss

8.2.5          Beekman's formula

8.2.6          The exact ruin probability in some simple cases

8.3           Discrete time model

8.3.1          The adjustment coefficient

8.3.2          Martingales and ruin

8.3.3          The impact of reinsurance on the adjustment coefficient