Aggregate Multivariate Monte Carlo | Vose Software

# Aggregate Multivariate Monte Carlo

### Introduction

The Aggregate Multivariate Monte Carlo window is a lot like the Aggregate Monte Carlo window, in that it directly calculates the sum of a random number of randomly sized variables.

However, in the Aggregate Multivariate Monte Carlo window you can enter multiple pairs of severity/frequency distributions to be added, and  optionally correlate the frequency distributions.

So, for example, you could model a portfolio of two related insurance policies (e.g. one for car accidents and one for trucks) aggregating a Poisson number of Lognormal-sized variables together with a Polya number of Normal-sized variables, and you can take into account that both have a correlated frequency (e.g. a bad winter will increase the number of accidents - claim events - for both)

A continuous distribution (e.g. a Gamma) can be fitted to the aggregate distribution (by matching moments), and this fitted distribution can in turn be inserted in the spreadsheet (see below).

To see the output functions of this window, click here.

### Window elements

On the upper left of the window is the list of Frequency/Severity distribution pairs. These should be discrete, respectively continuous Vose Distribution Objects.

To add a new distribution to the list, click anywhere in the white area. To remove a frequency/severity distribution pair from the list, select it (by clicking on it) and then click the x button on the right below the list.

In the correlation matrix shown, you can add correlation between the variance: double click a matrix element to add correlation (by default it is zero) between the two frequency distributions it corresponds to. Note that this correlation matrix is symmetrical, so changing one element will update the one on the other side of the diagonal accordingly.

Preview graphs for the frequency, severity and resulting aggregate distribution are shown.

• The preview graph of the aggregate distribution below has the following special buttons in its graphics toolbar:

•

• From left to right, these allow you to:

• Overlay one of several fitted distribution (by matching moments) to the calculated aggregate distribution.

• Insert the aggregate distribution in the spreadsheet in different ways.

• Insert the fitted overlay curve in the spreadsheet in different ways.

For explanations about other fields, buttons, graphs and summary statistics tables in this window, see

### Useful tips and tricks

See also: Graphics, workflow and error handling in ModelRisk

##### Using View Function to return to a window

The output of ModelRisk windows always corresponds to VoseFunctions (the functions ModelRisk adds to Excel) being entered into one or more spreadsheet cells.

You can always re-open the window for a ModelRisk function that is in a spreadsheet cell by using View Function. Select the spreadsheet cell and then select View Function from the ModelRisk menu/toolbar/ribbon.