Actuarial Outpost
Go Back   Actuarial Outpost > Exams - Please Limit Discussion to Exam-Related Topics > SoA/CAS Preliminary Exams > Short-Term Actuarial Math
FlashChat Actuarial Discussion Preliminary Exams CAS/SOA Exams Cyberchat Around the World Suggestions

Short-Term Actuarial Math Old Exam C Forum

Thread Tools Search this Thread Display Modes
Old 06-24-2018, 04:26 PM
alwaysseamus alwaysseamus is offline
Join Date: Jun 2013
College: Clemson University
Posts: 260
Default How to know when to use posterior vs. predictive for premium?

It seems like it's arbitrary whether to use posterior or predictive for the premium. I do notice that if the average of the distribution is value of the parameter that varies, than it makes sense for the posterior to be what we look at. For example, if x is exponential with theta, where theta is distributed as pareto.. Then we know that the expected value for theta will with the same as the expected value for x. Other than that, I'm a chicken with his head cut off, no idea.

Is there a resource out there that explains it well?
Reply With Quote
Old 06-24-2018, 06:32 PM
pershing pershing is offline
Join Date: Jul 2012
College: Starfleet Academy
Posts: 50

Let's say the loss amount follows an exponential distribution, given . The prior distribution of is single parameter Pareto(). 3 losses are observed, , and .


The experience is:

The posterior distribution of is:

Looks like an inverse Gamma to me, with and .

If you need posterior mean of , calculate :

If you need expected value of next claim, use the predictive distribution or double expectation, whichever is easier. In this case, the double expectation is much easier:


Hope this helps,
Reply With Quote
Old 06-24-2018, 09:49 PM
Academic Actuary Academic Actuary is online now
Join Date: Sep 2009
Posts: 8,422

If the likelihood is exponential, normal, Poisson, or bernoulli, there is a single parameter equal to the expected value. The mean of the posterior will be the mean of the predictive in these cases. If all you are interested in is the pure premium, you could use either mean. If you wanted some measure of risk you would need the predictive.
Reply With Quote

Thread Tools Search this Thread
Search this Thread:

Advanced Search
Display Modes

Posting Rules
You may not post new threads
You may not post replies
You may not post attachments
You may not edit your posts

BB code is On
Smilies are On
[IMG] code is On
HTML code is Off

All times are GMT -4. The time now is 09:09 PM.

Powered by vBulletin®
Copyright ©2000 - 2019, Jelsoft Enterprises Ltd.
*PLEASE NOTE: Posts are not checked for accuracy, and do not
represent the views of the Actuarial Outpost or its sponsors.
Page generated in 0.16303 seconds with 11 queries