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  #1  
Old 09-26-2016, 01:44 PM
leezard leezard is offline
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Default stratified sampling from catastrophe event table

I'm new to stratified sampling, though to my surprise it was mentioned in the Walters & Morin exam paper on catastrophes...

I'm working with capital modeling simulation software that samples from cat event tables provided by my internal cat modeling team. I want to stabilize the 1-in-1000-year tail results without running millions of iterations, so I thought stratified sampling might fit my purpose. Suppose I break up the space of possible annual cat losses into, say, 5 equal-probability strata of increasing annual losses, and produce separate event tables for each range, 10,000 events in each table. Then, depending on a random variable, sample from one of the strata to simulate one year's annual cat losses. Repeat 10,000 times. Will my simulation results do any better than randomly sampling from one 50,000-event table the same 10,000 times? Is this stratified sampling? I feel like I still face the same probability of simulating a 1-in-1000-year event, so my tail isn't any more stable...
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Old 09-26-2016, 04:22 PM
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You would take your 5 strata and sample from each one 2,000 times, giving you a total of 10,000 events.

One average this will give you the same number of tail events (e.g. in the worst 99.9% of the distribution) however the variability of the actual number of samples in the tail will decrease.

Sampling 10,000 times from the whole distribution means the number of events from the worst 99.9% of the distribution will have a binomial distribution with N=10,000 and p = 0.1%. So the mean number of events picked from the tail is 10,000 x 0.1% = 10, and the variance is 10,000 x 0.1% x 99.9% = 9.99.

Sampling in a stratified way means the number of events selected from the worst 99.9% of the distribution will have binomial distribution with N=2,000 (the number of samples taken from the worst strata -- the one containing the 80-100%-ile events -- since that's the only strata that can produce those tail events) and p = 0.1% / 20% = 0.5%. So the mean number of 99.9%-ile or worse events is 2,000 x 0.5% = 10 (still), but the variance is 2,000 x 0.5% x 99.5% = 9.95.

Not a massive difference, but that's a very small number of strata given that you're focusing on a very remote portion of the tail.
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Old 09-26-2016, 04:52 PM
leezard leezard is offline
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Gee thanks!

Building from your example, even 100 strata would only reduce the variance to 9.9, so divvying up the strata without increasing the total number of trials doesn't get me very far.

Looks like more trials are in my future...
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Old 09-26-2016, 07:22 PM
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Well, if you used 1,000 strata (with 10 samples from each) then you'd be certain of getting exactly 10 simulations from the worst 0.1% of your events (namely the 10 samples you picked from the worst stratum).

Going past that point won't further stabilize the number of tail events (because it can't), but would force the 10 tail simulations to be more evenly distributed across the tail.

At the extreme you could use 10,000 strata (one for each event you need to sample) -- each strata containing successive 0.01%-wide percentile layers of the data (with 5 cat events in each strata). You would sample one point from each stratum to get your sample data. Very little variability from one 10,000 point sample to the next, but you'd know that you were getting even coverage of the event distribution.

Of course if you're looking at total losses (losses from cats plus other sources) then getting a very uniform sample from the cat distribution won't make the total loss tail very stable unless cats are the dominant source of loss. Otherwise you'll still need to worry about the noise that's generated by the modeled correlation between the sources of losses.
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Old 01-05-2017, 02:41 AM
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You sampled from the Event Loss Table or the Yearly Loss Table from the cat model? If it's the former, I'm afraid the methodology is not so correct.
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