Each customer makes claims following a Poisson process with rate 0.44 per year. For Scheme A, there are 3 discount levels: 0%, 10% and 20%. For a customer in Scheme A, he or she will move between discount levels throughout the year at continuous times. The annual premium to be paid at the start of each year is determined by the discount level he or she is in at that point of time, irrespective of the movements between the discount levels throughout the year. If a customer in Scheme A makes a claim, he or she will immediately move to a worse discount level, if possible, or remain in the 0% level. Independently of the customer making claims, for each customer in Scheme A independently the insurance company will perform a 'bump' where the customer will move to a better discount level if possible (or remain iin 20% otherwise) every so often as a customer loyalty programme with time between bumps exponentially distributed with mean 2 years. Find the stationary distribution of customers in each discount level for Scheme A (in the order 0%, 10%, 20%)
This is a Stochastic Process question.
Each customer makes claims following a Poisson process with rate 0.44 per year.
For Scheme A, there are 3 discount levels: 0%, 10% and 20%.
For a customer in Scheme A, he or she will move between discount levels throughout the year at continuous times.
The annual premium to be paid at the start of each year is determined by the discount level he or she is in at that point of time, irrespective of the movements between the discount levels throughout the year.
If a customer in Scheme A makes a claim, he or she will immediately move to a worse discount level, if possible, or remain in the 0% level.
Independently of the customer making claims, for each customer in Scheme A independently the insurance company will perform a 'bump' where the customer will move to a better discount level if possible (or remain iin 20% otherwise) every so often as a customer loyalty programme with time between bumps exponentially distributed with mean 2 years.
Find the stationary distribution of customers in each discount level for Scheme A (in the order 0%, 10%, 20%)
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