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associate
08-31-2006, 09:59 AM
Is there a way to aggregate a fixed number of correlated severity distributions such that the aggregate distribution reflects the dependency structure - without using simulation techniques, like copula?

Can anybody help me? This is tightly related to DFA

no
08-31-2006, 04:32 PM
I do not understand your question clearly.

If you are saying:

1) You have ``n'' severity distributions and you know the correlation matrix
among these n distributions, then you want to specify the multivariate
distribution => copulas would be the only general method, but if you know
the correlations are positive you could use ``m'' (m>n) independent random
variables and add n-m random variables to remaining n. Simple example:
Y1=X1+Z
Y2 = X2 + Z, where X1,X2 and Z (>0) are independent random variables=> then
Y1 and Y2 are positively correlated

2) You want to model correlated losses => you could use time series model
or multivariate distributions.

associate
09-01-2006, 01:58 PM
Thanks,

My question focus on the 1) you mentioned. No frequency involved.

The big question is, can we somehow impose the severities'
dependency structure when using FFT's (not copulas, i.e. not
simulating)...The reason being, that when doing
calculations in the expected mode, my boss doesn't really
want to simulate.

associate
09-06-2006, 02:00 AM
Finally got a deal with boss.

If severity distributions are not correlated, we can use FFT to get the aggregated severity distribution; if related, use copula and simulation.

associate
09-06-2006, 02:05 AM
Forget one thing, if we know the correlation is linear, there will be no need for simulating. But usually people won't use linear. I will use Kandall's Tau or Spearsman's Rank instead.

MNBridge
09-08-2006, 10:07 PM
Forget one thing, if we know the correlation is linear, there will be no need for simulating. But usually people won't use linear. I will use Kandall's Tau or Spearsman's Rank instead.

Shaun Wang has a good paper out on this.

I'd add more but I'm just starting to use it. Did have an issue with the positive definite matrix.

I have 99 correlated variables.

Next step is figuring out best way to 'fix' that.
- Does reordering the variables help?
- Or will I just need to use the keep decreasing w until I get a positive definite matrix?

Thanks

Glenn Meyers
09-09-2006, 10:35 AM
Question - Why do you think the severities are correlated? I am not looking for an answer like "I just calculated a correlation matrix and I didn't see any zeroes." What is the underlying structure, e.g. inflation affecting all claims at once, of your correlation?

MNBridge
09-11-2006, 11:33 AM
Question - Why do you think the severities are correlated? I am not looking for an answer like "I just calculated a correlation matrix and I didn't see any zeroes." What is the underlying structure, e.g. inflation affecting all claims at once, of your correlation?

Is this to me?
Fitting Yields not severities.

I am finding the annual yield of a crop by County in a state (There are 99 counties in Iowa, my example).
- I think it easily passes the smell test that if one county has a low yield year an adjacent county will also have low yields for that year.

Sidenote: I did consider finding each counties correlation to the State Yield then simply using that. Except this would not consider the correlation of adjacent counties vs. ones on opposite sides of the state.

* Yield = yield per acre.

Glenn Meyers
09-11-2006, 08:50 PM
Fitting Yields not severities.

I am finding the annual yield of a crop by County in a state (There are 99 counties in Iowa, my example).
- I think it easily passes the smell test that if one county has a low yield year an adjacent county will also have low yields for that year.

Sidenote: I did consider finding each counties correlation to the State Yield then simply using that. Except this would not consider the correlation of adjacent counties vs. ones on opposite sides of the state.

* Yield = yield per acre.

I was hoping for something simpler, but I give this a shot.

Step 1 - list n scenarios where the expected yield varies by county. Some examples of scenarios include

1. Low yield for the entire state
2. High yield for the entire state.
3. Low yield for counties west of Des Moines, high yield for the counties east of Cedar Rapids, average yield for the rest of the state.

and so on.

Let pk be the probability of scenario k.

Come up with the distributions of actual yields abouth the average yield GIVEN SCENARIO k.

Let Phi_k be the FFT of the distribution of yields given scenario k.

The aggregate loss will be given by the inverse FFT of Sum(pk*FFT_k)

One addional thought - I am not sure it makes sense to aggragate yield per acre over the counties. How about total yield per county? However it still makes sense to use yield per acre in setting up the scenarios that drive the correlation.