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### Risk Aggregation

Posted: May 12th, 2016, 11:01 am
Hi,I wanted to aggregate two independent random variables-which depict the PnL numbers. The problem is that i dont have a ordered pair (i.e. a one to one mapping ) for the two random variables. I was thinking of using FFT or Panjer recursion but what i could find from my research is that it is applicable only for non-negative R.V.? I am not sure about this. Would be glad to hear some views on this.

### Risk Aggregation

Posted: May 12th, 2016, 1:06 pm
too vague -- use the eqn editor

### Risk Aggregation

Posted: May 12th, 2016, 1:21 pm
Hi, i will try and be more clear. I have two random variables X1 and X2 which have defined (but different) distributions. X1 and X2 can take any real number value. I want to calculate the probability of X1+X2<S where S is a real number. Could you please suggest some computationally efficient ways to do it. thanks.

### Risk Aggregation

Posted: May 12th, 2016, 3:56 pm
what's the distribution of (X1,X2)?

### Risk Aggregation

Posted: May 12th, 2016, 3:59 pm
This is an elementary math statistics question and can be found in any statistics for beginners handbook. Actually you need joint distribution function or an assumption which reduce joint distribution to single one say independence for X.

### Risk Aggregation

Posted: May 12th, 2016, 8:14 pm
Does "i dont have a ordered pair" mean the data is sparse (some samples of X1 have no corresponding X2 and some X2 lack an X1)?Are you sure they are "independent"? If they are, the problem is easy because you can characterize each distribution independently and then sum the two distributions. If they aren't independent, then you need to also characterize the joint distribution (and check that the missing samples aren't a function of the values).