Feldblum-1997 #30

[MichaelScarn]

This question asks us to decide if implementing a 5% renewal discount to improve retention is more profitable than not offering a discount, over the course of 4 years.

My first pass through the problem, I developed the premium for each year the same way: Premium * (1 + Prem Growth) * (1 - discount)

The model solution only shows the 5% renewal discount applying to the first year of renewals, when I thought it should be applied to each renewal period.

So when they talk about discounts for these types of problems (and don't specifiy the number of years the discount applies) are we supposed to assume that it only affects the first year?

[TOTEM]

If you follow the exhibits in the paper, that is how he applies the discount.

[2M]

The premium trends 6% a year with and without the discount.

In each renewal year after the 6% trend, you apply the 5% discount

[Vorian Atreides]

Originally Posted by MichaelScarn

The model solution only shows the 5% renewal discount applying to the first year of renewals, when I thought it should be applied to each renewal period.

So when they talk about discounts for these types of problems (and don't specifiy the number of years the discount applies) are we supposed to assume that it only affects the first year?

If I'm charged $100 as a new customer, but get a 5% discount for renewing with the company, I'm charged $95 at renewal. For simplicity, let's assume no rate changes and no increase in exposure or changes in loss propensity.

When I renew with the company again the following year, what will I be charged? Well, my basic premium is $100, but I get a 5% renewal discount. That's $95.

Note that the renewal discount for the third year that the policy is in force is not applied to the second year premium, but to the "new business premium". So, after the second year, the renewal discount should not be applied either at the individual level or the aggregate level.

If premium volume increases from year two to year three, the increase is applied to the already discounted premium.