Reinsuring an insurance policy

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Comes with one PDF document (26 pages), one unsolved Excel spreadsheet (Reinsuring an Insurance Policy unsolved .xlsx), one solved Excel spreadsheet (Reinsuring an Insurance Policy Solved.xlsx) and 8 videos with 32′ 09″ of training.



When an insurance company decides to reinsure portions of its risk portfolios it transfers to other parties by some form of agreement to reduce the likelihood of having to pay a large obligation resulting from an insurance claim.  In this contract, the party that diversifies its insurance portfolio is known as the ceding party. On the other hand, the party that accepts a portion of the potential obligation in exchange for a share of the insurance premium is known as the reinsurer.

A ceding insurance company decides to limit its unexpected losses by acquiring a policy with a reinsurer.  This is also called a stop-loss contract. Depending on the claims conditions of the ceding insurer’s policy and the conditions offered by the reinsurer, the cost of the reinsurance contract and the limitation of unexpected losses may or may not be convenient for the company. With @RISK it is possible to determine both probabilistic magnitudes. This case consists of the application of annual aggregate deductibles in which the reinsurer’s participation begins when the sum of the claims presented by the customer exceeds a certain amount.


We will use a frequency-severity model to help calculate the profit & loss statement that will let the insurer make a decision. A frequency-severity model is an actuarial method for determining the expected number of claims that an insurer will receive during a given time period, and how much the average claim will cost.

This type of method uses historical data to estimate the average number of claims and the cost of each claim. The simplified version of the method multiplies the average number of claims by the average cost of a claim.  We will demonstrate, however, that just the simple multiplication of the frequency component times the severity component will be just a rough approximation to the actual inherent risk at hand.  A convolution will come in handy to solve for this weakness as we will show.

Assume the following with respect to this policy. Historic data on accidents being reported for claims are detailed for the past years on the Accidents tab.   The average monthly premium charged per client is of $75 with a standard deviation of $5. Every month, new customers come in and some exit, leaving a constant average number of monthly customers at 2,200 with a 5% coefficient of variation.  A $400 deductible is considered on accidents being claimed.  The deductible is basically the amount “deducted” from an insured loss.

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Fernando Hernandez


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