Risk Modelling and Survival Analysis
Introduction
Motivation
1
R Setup
1.1
Preparing your environment
1.2
Basic interations with R
2
Loss distributions
Learning Objectives
Theory
2.1
Probability distributions for modelling insurance losses
2.2
Mechanisms for limiting insurance losses
2.3
Proportional and Excess of Loss reinsurance
2.4
Estimating parameters of loss distributions with complete data
2.5
Estimating parameters of loss distributions with incomplete data
R
Practice
3
Compound loss distributions
Learning Objectives
Theory
3.1
Modelling frequency of insurance claims
3.2
Modelling severity of insurance claims
3.3
Compound loss distributions
3.3.1
Compound binomial
3.3.2
Compound Poisson
3.3.3
Compound negative binomial
3.4
Compound loss distributions after reinsurance
R
Practice
4
Copulas
Learning Objectives
Theory
4.0.1
Characteristics of a copula
4.0.2
Gaussian copula
4.0.3
Archimedan family of copulas
R
Practice
5
Extreme value theory
Learning Objectives
Theory
5.1
Extreme value distributions
5.2
Calcuating and interpreting tail weights
R
Practice
6
Time series
Learning Objectives
6.1
Theory
6.2
Concept and properties of time series
6.3
Concept of stationary random series
6.4
Concept of a filter applied to a stationary random series
6.5
Notation for operators
6.6
The characteristic equation of time series
6.7
Concept and properties of random walks
6.8
Concept of a multivariate autoregressive model
6.9
Concept of cointegrated time series
R
Practice
7
Stochastic processes
Learning Objectives
Theory
7.1
Defining stochastic process
7.1.1
Defining a counting process
7.2
Classifying stochastic processes
7.2.1
Time basis
7.2.2
State space
7.2.3
Mixed type stochastic process
7.3
Applications of mixed processes
R
Practice
8
Markov chains
Learning Objectives
Theory
8.1
Features of a Markov chain model
8.2
Chapman-Kolmogorov equations
8.3
Stationary distribution for a Markov chain
8.4
Frequency based experience rating
8.5
Time-inhomogeneous Markov chain model
8.6
Markov chains in modelling
8.6.1
Simulating a Markov chain
R
Practice
9
Markov processes
Learning Objectives
Theory
9.1
Features of a Markov process model
9.2
Poisson process
9.3
Kolmogorov equations for a Markov process
9.4
Solving Kolmogorv equations
9.4.1
Simple cases
9.4.2
More general cases
9.5
Sickness and marriage models
9.6
Markov jump process
9.6.1
Simulating a Markov jump process
R
Practice
10
Survival models
11
Lifetime distributions
12
Estimating transition intensities
13
Graduation
14
Mortality projection
15
Machine learning
Learning Objectives
Theory
15.1
Machine learning topics
15.2
Machine learning from data
15.3
Supervised machine learning
15.4
Unsupervised machine learning
15.5
Penalised regression
15.6
Decision trees
15.7
Perspectives of non-actuarial professionals
R
Practice
A book by Alex Garbiak
Risk Modelling and Survival Analysis
Chapter 11
Lifetime distributions