SCMA469 Actuarial Statistics
1
Introduction to Stochastic Processes
1.1
Examples of real world processes
2
Review of probability theory
2.1
Random variables
2.2
Probability distribution
2.3
Conditional probability
2.4
Law of total probability
2.5
Conditional distribution and conditional expectation
2.6
Central Limit Theorem
3
Stochastic processes
3.1
Classification of stochastic processes
3.2
Random walk: an introductory example
4
Discrete-time Markov chains
4.1
One-step transition probabilities
4.2
The Chapman-Kolmogorov equation and
\(n\)
-step transition probabilities
4.3
Distribution of
\(X_n\)
4.4
Joint Distribution
4.5
Random walk with absorbing and reflecting barrier(s)
4.6
An example of nonhomogeneous Markov chain
4.7
Simulation
4.8
Monte Carlo Methods
4.9
Classification of states
4.10
Absorption probabilities and expected time to absorption
4.11
First step analysis
4.12
The expected time to absorption
4.13
The long-term distribution of a Markov chain
4.14
Stationary and limiting distributions for a single closed class
Stationary distributions
Proportion of Time in Each State
The method of finding the stationary distribution
4.15
Sufficient conditions for the long-run behaviour of a Markov chain
4.16
Limiting distributions
4.17
Main result
Applications of Markov chains to NCD systems
5
Poisson processes
5.1
Introduction
5.2
Poisson process
5.2.1
Counting Process
5.3
Properties of Poisson processes
5.4
Poisson process : Definition 2
5.5
Inter arrival times (Inter event times or holding times)
Important result
5.6
Superposition and thinning properties
Superposition property
Splitting (Thinning) property
5.7
Memorylessness
6
Tutorials
6.1
Tutorial 1
6.2
Tutorial 2
6.3
Tutorial 3
6.4
Tutorial 4
6.5
Tutorial 5
6.6
Tutorial 6
6.7
Tutorial 7
7
Applications
7.1
DataCamp Light
8
Final words
8.1
DataCamp Light
References
Published with bookdown
SCMA469 Actuarial Statistics
References