Actuarial Outpost SOA #304
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#1
01-27-2014, 09:09 PM
 unam Member Join Date: Aug 2008 Posts: 39
SOA #304

Looking at this question - are the random numbers generated for discrete random variable J given in part a) just extraneous information?
#2
01-27-2014, 09:16 PM
 Gandalf Site Supporter Site Supporter SOA Join Date: Nov 2001 Location: Middle Earth Posts: 31,073

No. You need them to know the mean of the exponential distribution for that particular claim.
#3
01-28-2014, 08:37 AM
 MastaJ773 Member SOA AAA Join Date: Nov 2012 Posts: 313

This was the most convoluted question I could've imagined. Really? 2/3rds of a page when you could've just said "Determine the mean of 3 stochastic RVs"?
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#4
01-28-2014, 10:34 AM
 Gandalf Site Supporter Site Supporter SOA Join Date: Nov 2001 Location: Middle Earth Posts: 31,073

Quote:
 Originally Posted by MastaJ773 This was the most convoluted question I could've imagined. Really? 2/3rds of a page when you could've just said "Determine the mean of 3 stochastic RVs"?
Really? How much shorter could it be? You are determining the sample mean, not the mean, otherwise no simulation aspect.

You do have to describe the distribution of the random variables, and then describe how the sample values are simulated from that distribution.

Admittedly the following question would be much simpler and would also test the sample mean, but the actual question has much more content, not just lots more words.
Quote:
 You roll three dice. The results are 1,2,6. Determine the sample mean of the three rolls.
#5
06-22-2018, 10:02 PM
 ericp Member Join Date: Aug 2007 Posts: 283

In this problem we're using random numbers to select one of four distributions with means of 1.0, .75, .5 or .25, then we using other random numbers to generate a random value from the chosen distribution? At least that's what it looks like to me.
What kind of real world losses would a simulation like this one be used for?
#6
06-23-2018, 09:47 AM
 Gandalf Site Supporter Site Supporter SOA Join Date: Nov 2001 Location: Middle Earth Posts: 31,073

I donīt know how much of the material you have covered. By far the most common type of multi-step simulation, I suspect, would be first simulate the number of claims, then simulate the magnitude of the claims (possibly simulating the magnitude of the claims individually).

Another possibility, which may or may not ever be used, would be for a health insurer to first simulate whether it would be a mild flu season, a bad flu season, or an epidemic, and then simulate its claims cost conditional on the type of season.
#7
06-23-2018, 11:36 AM
 ericp Member Join Date: Aug 2007 Posts: 283

Ah, interesting. Thanks for that explanation Gandalf.