
Modelos Setoriais |
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@RISK is widely used in insurance and reinsurance for premium pricing and loss reserves modeling. A 2006 survey identified @RISK as the third most widely-used software by actuaries, after Microsoft Office and in-house actuarial tools. Download and install a free trial version of @RISK to view the models in full.
Suppose that the company is required by law to have enough money on hand to pay all the claims with the probability of 95%, and that it can only set aside $2000 for the purposes of this particular insurance product. On the other hand, a simulation of the model shows that the 95th percentile of the Total Payment Amount is around $2700. Assume further that the company can purchase from a larger company an insurance policy against the number of claims being in the top decile. The policy under consideration specifies that if the number of claims falls within the top decile, the larger company will satisfy all the claims. The smaller company can model the situation with the policy in place by using Stress Analysis to stress the distribution for total number of claims from the 0th to 90th percentile. With the modified distribution the 95th percentile of the Total Payment Amount is reduced to around $1650. If the policy costs up to $350, the smaller company can purchase it and keep $1650 on hand to comply with the law. Would the larger company be willing to sell the policy for under $350? There is a 10% probability that it will be required to make payments under the policy. The payments can be analyzed using the same model and stressing the distribution for total number of claims from the 90th to 100th percentile. This analysis shows the mean payment to be around $2800. Since there is only a 10% probability that claims will need to be satisfied, the mean cost to the larger company is around $280. Hence, it does not seem unreasonable for the larger company to sell the policy for $350.
Possible generalizations to this model that could be made (and which are explored in more detail on Palisade training courses) include: a) Assessing the impact of changing the loss resulting from each event into a distribution, rather than assuming a fixed amount. b) Assessing the impact if mitigating actions could be developed for certain events, so that, e.g., the amount of loss were reduced if these events occur (or the probabilities of events are reduced or both). c) Creating dependencies or correlations between the occurrence (and/or magnitude) of some of the events. d) Replacing the Binomial distribution with a Poisson distribution so that each event could occur more than once per period.
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Praia de Botafogo,
nº 501 Sala 101, Botafogo
22250-000 Rio de Janeiro-RJ
+55 (21) 3958 1443
+1 607 277 8000 x318 tel
800 432 7475 x318 E.U.A.
vendas@palisade.com
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+1 607 277 8000 x318
800 432 RISK (EEUU/Canadá)
+1 607 277 8001 fax
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+56 2581-3492 Chile
+507 836-5675 Panamá
+52 55 5350 2852 México
+51 1 708-6781 Perú
+57 1 508-5187 Colombia
servicioalcliente@palisade.com
ventas@palisade.com
www.palisade-lta.com
+1 607 277 8000 x318
800 432 RISK (EEUU/Canadá)
+1 607 277 8001 fax
+54 (11) 5252-8795 Argentina
+56 2581-3492 Chile
+507 836-5675 Panamá
+52 55 5350 2852 México
+51 1 708-6781 Perú
+57 1 508-5187 Colombia
servicioalcliente@palisade.com
ventas@palisade.com
www.palisade-lta.com