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Download a pdf copy of this help file here |
=VoseRunoff(N, TimeObject,{TimeStamps},ClaimsizeObject)
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))).
You have 1000 agreed sales. Each sale will generate Lognormal(1.7,3.4) $k, but will take Weibull(2.6,4.3) weeks to complete. What does the income stream look like? The answer is shown in this example model:
A 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 
Runoff1
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.
Imagine that the Poisson(121) generates a value of 115. The VoseRunoff function then generates 115 values sampled from the time until payout distribution (Lognormal(0.7,1.4) in this example) and 115 values from the claim size distribution (Pareto(5,2) in this example). It sorts each payout time into the bins defined by the TimeStamp array and sums the corresponding claim sizes for each bin to give the output values.
Note the VoseRunoff algorithm assumes that the claim size and time until
payout are considered independent. This may not be true. For example,
where a very large claim occurs there may be some considerable dispute
between the insured and insurer which could protract the time until payout.
In this situation, it would be better to separate claims out into different
strata where each stratum is a range of claim sizes with an appropriate
Payout time distribution, and then sum the resultant payout streams,
as shown in the example model Runoff2.
The VoseRunoff function uses Distribution Objects for the claim size
and time until payment. Historic data will usually be available for these
variables, in which case one can use fitted distribution objects to directly
refer to the data, as shown
in the example model Runoff3.