The basics of Stochastic Processes and Markov Chains
In this course we look at Stochastic Processes, Markov Chains and Markov Jumps
We then work through an impossible exam question that caused the low pass rate in the 2019 sitting.
This question requires you to have R Studio installed on your computer.
Things we cover in this course:
Section 1
- Stochastic Process
- Stationary Property
- Markov Property
- White Noise
- Increments
- Random Walks
Section 2
- Markov Chains
- Transition Probabilities
- Chapman-Kolmogorov Equations
- Transition Matrix
- Stationary Probability Distributions
- Irreducibility
- Periodicity
Section3
- R Studio Exam Question
Section 4
- Markov Jump Process
- Transition and Survival Probabilities
- Kolmogorov’s Forward Differential Equation
- Transition Rates
- Generator Matrix
- Kolmogorov’s Backward Differential Equation
Stochastic Processes
1
Introduction to Stochastic Processes
2
Stationary
3
Increments
4
Markov Property
5
White Noise
6
Random Walk
7
Poisson Distribution
8
Poisson Process
9
Compound Poisson Process
Markov Chains
1
Markov Chains
2
Transition Probabilities
3
Chapman-Kolmogorov Equation
4
Transition Matrix
5
Transition Matrix Example with R Code
6
State Modification Trick
7
Stationary Probability Distributions
8
Irreducibility
9
Periodicity
R Past Exam Question
1
Installing R and Set up
2
R basics for Actuaries - Part 1
3
R basics for Actuaries - Part 2
4
Understanding the Question
5
Question 1 Solution
6
Question 2 Solution
7
Question 3 and 4 Approach
8
Question 3 Solution
9
Question 4 Solution
10
Question 5 Solution
Markov Jump Processes
1
Introduction to Markov Jumps
2
Transition and Survival Probabilities
3
Assumptions for Kolmogorov's Forward Differential Equation
4
Kolmogorov's Forward Differential Equation
5
Solving Kolmogorov's Forward Differential Equation
6
Transition Rates and Generator Matrix
7
Kolmogorov's Backwards Differential Equation
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