Recursive relatioonships between reserves

[Molly]

Hi all,

Am a little confused here on why the recursive relationships for reserves does not treat renewal expenses as "expected claims plus expenses paid at t+1". for example im looking at chapter 20 question 7:

I do not understand why c does not need to be included in both sides of the equation, and also why k does not need to be included in both sides?

K is the renewal expense, since we will have to renew at t+1 i would have thought we would need this? Also c is a claim expense, we will need this if there is a claim at time t right?

Thanks

 

[Richie Holway]

Hi Molly,

With these recursive reserves, we are looking at periods of 1 year each time. And for each 1 year of a policy, there is only 1 premium for that policy year, only 1 renewal expense in relation to that policy year, and only 1 point in time when a claim can be paid for that policy year.

So for policy year 5 say (that's the year that starts at time 4 and ends at time 5): the premium for the year will be paid at the beginning (time 4), the renewal expense for the year will be at the beginning (time 4), the claim (if due) will be payable at the end (time 5), and so the claims expense will also be incurred (if there is a claim) at time 5 too.

You're right that there is also a possible claim at time 4, say, but this would be in respect of deaths in policy year 4, and hence we don't consider them in the above example. A similar argument can be made for the renewal expense at time 5: that will be in respect of policy year 6, whereas in the above example, we are only interested in policy year 5.


Thanks,
Richie

 

[Molly]

Hi Molly,

With these recursive reserves, we are looking at periods of 1 year each time. And for each 1 year of a policy, there is only 1 premium for that policy year, only 1 renewal expense in relation to that policy year, and only 1 point in time when a claim can be paid for that policy year.

So for policy year 5 say (that's the year that starts at time 4 and ends at time 5): the premium for the year will be paid at the beginning (time 4), the renewal expense for the year will be at the beginning (time 4), the claim (if due) will be payable at the end (time 5), and so the claims expense will also be incurred (if there is a claim) at time 5 too.

You're right that there is also a possible claim at time 4, say, but this would be in respect of deaths in policy year 4, and hence we don't consider them in the above example. A similar argument can be made for the renewal expense at time 5: that will be in respect of policy year 6, whereas in the above example, we are only interested in policy year 5.


Thanks,
Richie

Hi Richie,

Thank you so much for this, i hadnt been thinking of these in terms of when the payments (whether that be premiums or expenses) are made, but it makes much more sense to me to do it this way.

Thank you!
Molly