Overview
Individual portfolio models are models that model each contract in the portfolio individually, (see single insurance policy analysis ) and then take the sum of the outcomes of the individual contracts to be the portfolio outcome.
{% S = \sum_{i=1}^n X_i %}
If the number of claims and claim sizes are not independent, that is, they are correlated in some way,
the modeling of each claim must account for this correlation.
Computing the Sum
Once the individual policies within a portfolio have been modeled, (see single insurance policy analysis ) the next step in the portfolio analysis is to sum these variables. This can be done in one of two ways.
- Sum of Random Variables The distribution of a variable which is a sum of random variables is calculated as a convolution. (see Sum of Random Variables )
- Monte Carlo
Comparison to Loan Default
The modeling of an individual policy is very similar to the standard modeling framework used to model laon default, PD, LGD, EAD. One can translate the variables from one framework to the other as follows.
- PD (Probability of Default) translates to Probability of a Claim
- LGD (Loss Given Default) translates to Claim Amount
- EAD (Exposure at Default) translates roughly to Policy Limit