If we test the difference between these two trends statistically, they are not significantly different. Setting them equal will give a correlation of 1 between the two trends -a “worst” case scenario. The correlation between the residuals reduces the diversification benefit, i.e. the standard deviation of the aggregate reserve distribution is higher than you would estimate if you assumed they were completely unrelated. The correlation between the trends may either reduce or increase the diversification benefit. In this case, it has little effect. Forecasting with this model, we find the aggregate outstanding reserve distribution (of the two lines) has a coefficient of variation of 13%. With the more optimistic assumption of no relationship, the coefficient of variation is lower at 11%. Using the composite model, we can run a simulation to find the full probability distribution of the aggregate outstanding. From this, we can find percentiles of the distribution (e.g. the value that has a 75% probability of being adequate), Value-at-Risk, and evaluate reinsurance options. Similar distributions can be produced for accident period totals and calendar period totals.

Coefficient of variation of aggregate

Dynamic Financial Analysis

All the information that you need for Dynamic Financial Analysis is provided. Correlations are calculated between lines of business on both dollar scale and on the log scale, for the total outstanding, as well as for individual accident or calendar period totals. Note that these correlations relate to the information in your data, which may be very different to other companies or the industry. Simulated values are produced for accident totals, calendar totals and the total outstanding, for each triangle and for the aggregate. These values provide you with the necessary input of loss distributions for DFA software.

Capital Allocation
The calculated correlations and standard deviations can be used to decide how capital should be allocated between lines of business. The formula suggested in Brehm, “Correlation and the Aggregation of Unpaid Loss Distributions”, CAS 2002 Forum, is used in the Forecast Summary to give the proportion of excess capital to be allocated to each line, by total, accident year or calendar year.