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ibnr

Compute IBNR claims for expectedClaims object

Description

example

ibnrClaims = ibnr(ec) computes the incurred-but-not-reported (IBNR) claims for an expectedClaims object.

Examples

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Compute the IBNR claims for an expectedClaims object containing simulated insurance claims data.

load InsuranceClaimsData.mat;
head(data)
ans=8×4 table
    OriginYear    DevelopmentYear    ReportedClaims    PaidClaims
    __________    _______________    ______________    __________

       2010             12               3995.7          1893.9  
       2010             24                 4635          3371.2  
       2010             36               4866.8          4079.1  
       2010             48               4964.1            4487  
       2010             60               5013.7          4711.4  
       2010             72               5038.8          4805.6  
       2010             84                 5059          4853.7  
       2010             96               5074.1          4877.9  

Use developmentTriangle to convert the data to a development triangle, which is the standard form for representing claims data. Create two developmentTriangle objects, one for reported claims and one for paid claims.

dT_reported = developmentTriangle(data,'Origin','OriginYear','Development','DevelopmentYear','Claims','ReportedClaims')
dT_reported = 
  developmentTriangle with properties:

                          Origin: {10x1 cell}
                     Development: {10x1 cell}
                          Claims: [10x10 double]
                  LatestDiagonal: [10x1 double]
                     Description: ""
                      TailFactor: 1
    CumulativeDevelopmentFactors: [1x10 double]
               SelectedLinkRatio: [1x9 double]

dT_paid = developmentTriangle(data,'Origin','OriginYear','Development','DevelopmentYear','Claims','PaidClaims')
dT_paid = 
  developmentTriangle with properties:

                          Origin: {10x1 cell}
                     Development: {10x1 cell}
                          Claims: [10x10 double]
                  LatestDiagonal: [10x1 double]
                     Description: ""
                      TailFactor: 1
    CumulativeDevelopmentFactors: [1x10 double]
               SelectedLinkRatio: [1x9 double]

Create an expectedClaims object where the first input argument is the reported development triangle and the second input argument is the paid development triangle.

earnedPremium = [17000; 18000; 10000; 19000; 16000; 10000; 11000; 10000; 14000; 10000];
ec = expectedClaims(dT_reported, dT_paid,earnedPremium)
ec = 
  expectedClaims with properties:

         ReportedTriangle: [1x1 developmentTriangle]
             PaidTriangle: [1x1 developmentTriangle]
            EarnedPremium: [10x1 double]
            InitialClaims: [10x1 double]
          CaseOutstanding: [10x1 double]
    EstimatedClaimsRatios: [10x1 double]
     SelectedClaimsRatios: [10x1 double]

Use ibnr to compute the IBNR claims.

ibnrClaims = ibnr(ec)
ibnrClaims = 10×1
103 ×

   -0.0984
   -0.0176
   -0.0399
    0.0030
    0.0204
    0.1483
    0.1753
    0.2744
    0.6423
    1.6575

Input Arguments

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Expected claims, specified as a previously created expectedClaims object.

Data Types: object

Output Arguments

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IBNR claims, returned as an array.

More About

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IBNR

Incurred-but-not-reported (IBNR) claims are the claims amount owed by an insurer to all valid claimants who have had a covered loss but have not yet reported it.

Since the insurer knows neither how many of these losses have occurred nor the severity of each loss, IBNR is necessarily an estimate.

Introduced in R2020b