Loss reserving is very important for property and casualty insurance companies. For insurance policies that cover all damages or injuries occurred during the insured period the claims may be made or fully regulated considerably after the insurance term. Future pay-outs have to be estimated for incurred but not reported (IBNR) claims to ensure that sufficient reserves are set aside that will cover the aggregate claim cost with a certain probability. The usual classification for IBNR is occurrence year versus reporting year and expected costs are determined for each combination. However, this does not give a sense of the distribution of costs over time nor their interdependence.
The VoseRunOff array function allows the stochastic modeling of costs over any desired period. Use this function to model a number N of payment events appearing at random points in time, where each event can take a random size. VoseRunOff then models the total amount of payment appearing at each year/month ... depending on the timestamps. The function parameters are as follows (using year as the nominal measure of time):
- TotalClaims (n) - the total number of claims predicted to occur from a policy in a certain occurrence year
- TimeObject - a distribution object describing the time from occurrence year until the year of payout
- TimeStamps - an array of increasing points in time at which the payouts will occur
- ClaimSizeObject - a distribution object describing the possible size of a claim
You can also use this function to just count the number of events (instead of their total size) happening at the timestamps by using a ClaimSizeObject that always returns 1 (E.g. VoseBernoulliObject(1))). The following examples are illustrated in different sheets of the Runoff example model.
Example 1 – Payout of random claimsA total of Poisson(121) claims are expected to occur from events occurring last year but not yet reported. The time until payout of a random claim follows a Lognormal(0.7,1.4) years distribution. The size of a random claim in $1000 follows a Pareto(5,2) distribution. We wish to model the payout per quarter for the next five years.
The example model sheet Runoff 1 illustrates how this is implemented in ModelRisk. Note that the VoseRunoff function extends one cell beyond the TimeStamp array to show the total cost of all claims that will occur beyond the last defined time point: