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DFA Insurance Company Case Study, Part I: - page 19 / 40

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Expenses, other than the loss adjustment expenses already incorporated into the loss ratios, were modeled as both fixed and variable. Actual values were again obtained through a combination of company-specific and industry statistics.

Property

0.4

0.4

1.0

GL

0.4

0.5

0.6°

t .0

Other

0.2

0.3

0.3

0.3

We have already discussed some of the randomness modeled into the projected core loss ratios. Further randomness is introduced to the model through the sensitivity of losses, expenses, and premiums to unexpected changes in the level of inflation. For DFAIC, we modeled the losses and fixed expenses as being immediately and fully responsive to unexpected changes in the level of inflation while premiums were partially responsive after a one-year time lag. Inflation sensitivity introduces a stochastic element affecting loss ratios, expenses, premiums, and payment patterns.

1.0

WC

Auto

WC

1.0

Auto

0.3

1.0

The simulations include a reasonable level of positive correlation between lines of business as indicated in Table 5.

Table 5: Ultimate Loss Ratio Correlation Coefficients

Property

GL

Other

"Note that the GL/Property correlation coefficient is artificially inflated because CMP less ratios are a component of the loss ratios for both lines.

Such positive correlation between lines of business is commonly accepted. It is probably the result of several factors, including changes to overall pricing levels in the insurance market and unanticipated inflation impacting the loss ratios of all lines of business.

Assumptions concerning correlation between lines of business are part of a series of parameter assumptions important within the context of building an appropriate DFA model. Because of our inability to access DFAIC for further information, it is especially important that our assumptions ~re reasonable both in isolation and in conjunction with other assumptions. For example, our collective risk model for generating workers compensation losses gross of reinsurance appears reasonable when compared to industry and available DFAIC statistics. But just as important, when we used this loss model to develop pricing for the current workers compensation excess of loss cover, the indicated reinsurance premium was comparable to that indicated by DFAIC Annual Statement exhibits. Such observed consistencies build confidence in the model and its assumed parameter values.

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