1. There are four basic components of estimating the premium to be charged; firstly the risk premium, secondly the direct policy related expenses, thirdly a contribution to fixed overhead expenses and finally a profit margin.
2. The industry partices with profit load and risk premium relativities for different customers being combined in some way. Consequently, in a competitive market, marketing discounts and/or rating action in response to competition become indistinguishable from rating action taken in response to changing claims experience.
3. if it were possible to anticipate an individual customer's response to the new business or renewal terms offered, then a probabilistic approach could be adopted in setting both the contribution to overheads and the profit margin in order to maximise expected profit.
4. The model needs to be flexible enough to take into account the individual characteristics of each policyholder and be able to respond to the dynamics of the market place. Under certain market conditions or market segments it is quite plausible that the profit loads can be negative.
GLM FUNCTIONS
1. Demand curves are generally naturally downward sloping, and the shape and level of the curve depends of the individual characteristics of each customer, on the pricing action taken over last year (for renewal business), and on the competitive positioning of the market segment involved. The level and shape of the curve will also be significantly different for new business quotations and rcnewal quotations. The demand for insurance (be it from new business or for renewing policies) for any individual customer is given by the following graph.
2. The contribution curve is a 45 ° line anchored at a point Po. Po represents the expected claims cost arising from the policy (i.e. the risk premium) plus an allowance for direct expenses associated with the policy. P0 is often referred to as the "breakeven" premium. P0 is very heavily dependent on the risk characteristics associated with each policyholder, because the expected claims costs and associated expenses are heavily dependent on the policyholder. Given that a policy has been written at premium level Pi, the contribution to fixed costs and profit will simply be Pt - Po. Ignoring fixed expenses, the contribution curve for a policy looks as follows:
3. One possible way of building an allowance for fixed expenses into the rating structure is to carry out some form of projection of business volume and convert this to a per policy cost. if more business than expected is written the per policy contribution to fixed costs reduces.
4. If a particular policy had a high probability of conversion/renewal compared to average, then the policy contributes a greater expected amount towards fixed costs than if the probability of conversion/renewal was expected to be lower than average. Building in fixed expenses in this manner has the intuitive appeal of attracting policyholders with higher persistency rates. The graph below gives a typical shape of fixed expense curve.
5. Given the basic components of lhe demand function and the corresponding costs, it is possible to combine these in order to generate an expected profits curve. The price that equates to the maximum profit can easily be derived. Alternative scenarios can easily be calculated by optimising other suitable functions which may place greater value to certain components of the process The shape of the resulting curve is given in the graph below:
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