risk - Get distribution for aggregate loss using Monte Carlo

I am given two data sets containing dates and losses (in some currency).

Given a distribution for the amount of losses and an (a,b,0) distribution for frequency of losses, how can I use Monte Carlo simulations to get a distribution for aggregate losses?

The papers and books I see online seem to state how to simulate aggregate losses (by simulating # of losses and losses given such #), but how do I come up with a distribution given all that data?

There's this book I found "Operational Risk with Excel and VBA". It describes the procedure and ends with the mean, standard deviation and other moment stuff. Is that sufficient to describe the distribution of aggregate losses?

Cross-posted: https://stats.stackexchange.com/questions/136541/get-distribution-for-aggregate-loss-using-monte-carlo

Answer

You can do the following:

• For each $i$ in $1$ to number of Mont-Carlo runs $K$


• simulate the number of losses $N_i$



• simulate $N_i$ many loss-sizes $X_{i,1},\ldots,X_{i,N_i}$


• calculate $L_i = \sum_{j=1}^{N_i} X_{i,j}$

Doing this you get a sample of losses $L_1,\ldots,L_K$ and you can do all sorts of hisograms, density fits, VaR, ES calculations on it.

EDIT: on this sample you could try to fit a loss distribution (e.g. Gamma or translated Gamma see here) by maximum likelihood or method of moments. But you can apply the method of moments even without MC becauase if you assume that the number of losses and the loss sizes are independent then $$ E[L] = E[N]E[X] \text{ and } V[L] = E[N]V[X] +E[X]^2 V[N] $$ for these fromulas and fitting distributions see e.g. again here.