CT4 Markov Chains

Question 1

State the essential features of a Markov chain model.

Answer 1

a) Exhibits the Markov property
b) Has a discrete state space
c) Operates in discrete Time domain

A No Claims Discount scheme is an example of a Markov Chain. Its very popular in the Exam.

Question 2

State the Chapman-Kolmogorov equations that represent a Markov chain.

Answer 2

Pij(m,n) = sum Pik(m,l) *Plk( ln)

Question 3

What do u understand by Stationary Distribution of a Markov Chain?

Answer 3

A Markov Chain is said to have a stationary distribution if the statistical properties of the process don’t change over time.

Question 4

Describe a system of frequency based experience rating in terms of a Markov chain and
describe other simple applications.

Answer 4

1

Question 5

Describe a time-inhomogeneous Markov chain model and describe simple applications.

Answer 5

2

Question 6

Demonstrate how Markov chains can be used as a tool for modelling and how they can
be simulated.

Answer 6

3