1. Hi guys,

Got a complex question regarding markov chain modelling.

I'll start off with an example. Say you own a credit card and you can only ever be in 3 states.
1)non-user - you're currently not using your credit card
2)full payer - you pay off your balance in full each month
3)partial payer - you only pay some of your balance off eg. 50%, 60% etc.

I'm not having any problems calculating the probabilities of moving from one state to the next. i just dont know how i would use these probabilities to calculate someone's expected outstanding balance on their credit card.

Any ideas or help?

Much appreciated

2.

3. Originally Posted by ace123
Hi guys,

Got a complex question regarding markov chain modelling.

I'll start off with an example. Say you own a credit card and you can only ever be in 3 states.
1)non-user - you're currently not using your credit card
2)full payer - you pay off your balance in full each month
3)partial payer - you only pay some of your balance off eg. 50%, 60% etc.

I'm not having any problems calculating the probabilities of moving from one state to the next. i just dont know how i would use these probabilities to calculate someone's expected outstanding balance on their credit card.

Any ideas or help?

Much appreciated
There are probably some things you are not telling us. Like an assumed interest rate and and assumed rate of expenditure if you are using your card. So lets say that someone using a card spends 1 (insert your favorite units) per month. Let I be the monthly interest rate charged by the card, levied agains the average balance for the month. This question would also be dependent on the number of months that have passed since the start, call that n.

A non-user would have an outstandidng balance per month of 0.

A full payer would have and averager outstanding balance per month of 0.5.

A partial payer, at the end of period n+1 with starting Balance Bn would have an ending balance
B(n+1) = (Bn +1)+I(Bn +.5)

and an averabe balance during the month of [B(n+1) + Bn]/2.

Now I think you can model this using what you know about probabilities for changing states.

4. Hi DrRocket,

Ok say for example a customer, at the end of month 0, has a balance of £50. His average spend per month is £5 and the monthly interest rate is 0.5%.

Also at the end of month 0 the customer is sitting as a partial payer - state 3.

The prob of going from :

State 3 to 3 is 60% (partial payer to partial payer)
State 3 to 2 is 30% (partial to full)
State 3 to 1 is 10% (partial to non-user)

Say we wanted to look at the projections for the next 12 months.

How would i use the above scenario using your formula?

Thanks

5. Originally Posted by ace123
Hi DrRocket,

Ok say for example a customer, at the end of month 0, has a balance of £50. His average spend per month is £5 and the monthly interest rate is 0.5%.

Also at the end of month 0 the customer is sitting as a partial payer - state 3.

The prob of going from :

State 3 to 3 is 60% (partial payer to partial payer)
State 3 to 2 is 30% (partial to full)
State 3 to 1 is 10% (partial to non-user)

Say we wanted to look at the projections for the next 12 months.

How would i use the above scenario using your formula?

Thanks
Hold on a minute. You started this with a statement that indicated that you knew something about Markov processes. I thought you were looking for a hint as to how to proceed with your model. I am not going to do your homework for you.

6. Calculating the probabilities is the markov chain process. and YES of course i know about markov chains. I just dont know how to APPLY these probabilities to calculate an expected balance

do you get where i'm coming from?

you quoted in saying "A full payer would have and averager outstanding balance per month of 0.5. "

where did the 0.5 come from?

I thought if i illustrated the scenario using my figures it would make a bit more sense to me.........

7. So you have calculated the stationary distribution?

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