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DFA Insurance Company Case Study, Part I: - page 15 / 40





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DFAIC's current reinsurance program and its implications for parameterizing our DFA model.

DFAIC's current reinsurance program includes excess of loss coverage for property, liability, and workers compensation risks, as well as coverage for catastrophes. In order to model the effects of these and alternative treaties, we generated individual large losses and occurrences on a gross of reinsurance basis. This necessitates the development of both frequency and severity probability distributions within the context of a collective risk model. Both company-specific and industry experience were gathered and analyzed for this purpose. Once the collective risk model was ready, individual large losses and catastrophes were generated stochastically and reinsurance covers were applied to obtain simulated losses net of reinsurance. Normally, company management would be consulted before finalizing company specific assumptions such as reinsurance arrangements or the frequency and severity of large losses and catastrophes.

In setting up our model, we condensed DFAIC's business into five distinct lines: Workers Compensation, Auto Liability (both personal and commercial), Property (homeowners and CMP property coverage), General Liability (other liability, product liability, special liability, and CMP liability coverage), and All Other (predominantly auto physical damage). Segregation of business into these five lines allows for the effective modeling of reinsurance programs without burying results within a mass of detail. Each of these five lines is assigned a set of descriptive parameters to appropriately model its constituent line of business. Needed parameterizations relate to such items as premiums, losses (including loss adjustment expenses), other expenses, and payment patterns, as well as their stochastic properties. A preliminary step in our analysis involved restating historical results to be consistent with our five modeled lines of business TM.

Projections of expected future premiums and loss ratios are in part based upon our assumed future business plans for DFAIC. An analysis of DFAIC's Schedule P reveals a recent deterioration Jn underwriting results and earned premium Jevels. Such a situation might indicate past DFAIC rate reductions made in an attempt to maihtain market share within a competitive environment. Falcon's business plan would be to raise rates thereby restoring loss ratios to DFAIC historical levels in three to five years. Anticipated effects of this business plan are reflected in our parameterization of future written premium levels.

14E.g. CMP results were segregated into properly or casualty and allocated to our Property or General Liability lines of business, respectively.


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