ibnr

Compute IBNR claims for bornhuetterFerguson object

Syntax

ibnrClaims = ibnr(bf)

ibnrClaims = ibnr(___,referenceClaimsType)

Description

ibnrClaims = ibnr(bf) computes incurred-but-not-reported (IBNR) claims for reported or paid claims for a bornhuetterFerguson object.

ibnrClaims = ibnr(___,referenceClaimsType) additionally specifies the type of claims data. Specify this argument after the input argument in the previous syntax.

Examples

Compute IBNR Claims for bornhuetterFerguson Object

Compute IBNR for either reported or paid claims for a bornhuetterFerguson object containing simulated insurance claims data.

load InsuranceClaimsData.mat;
head(data)

    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: {10×1 cell}
                     Development: {10×1 cell}
                          Claims: [10×10 double]
                  LatestDiagonal: [10×1 double]
                     Description: ""
                      TailFactor: 1
    CumulativeDevelopmentFactors: [1.3069 1.1107 1.0516 1.0261 1.0152 1.0098 1.0060 1.0030 1.0010 1]
               SelectedLinkRatio: [1.1767 1.0563 1.0249 1.0107 1.0054 1.0038 1.0030 1.0020 1.0010]

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

dT_paid = 
  developmentTriangle with properties:

                          Origin: {10×1 cell}
                     Development: {10×1 cell}
                          Claims: [10×10 double]
                  LatestDiagonal: [10×1 double]
                     Description: ""
                      TailFactor: 1
    CumulativeDevelopmentFactors: [2.4388 1.4070 1.1799 1.0810 1.0378 1.0178 1.0080 1.0030 1.0010 1]
               SelectedLinkRatio: [1.7333 1.1925 1.0914 1.0417 1.0196 1.0097 1.0050 1.0020 1.0010]

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

Create a bornhuetterFerguson object with reported claims, paid claims, and expected claims to calculate ultimate claims, cases outstanding, IBNR claims, and unpaid claims estimates.

bf = bornhuetterFerguson(dT_reported, dT_paid, ec.ultimateClaims)

bf = 
  bornhuetterFerguson with properties:

     ReportedTriangle: [1×1 developmentTriangle]
         PaidTriangle: [1×1 developmentTriangle]
       ExpectedClaims: [10×1 double]
    PercentUnreported: [10×1 double]
        PercentUnpaid: [10×1 double]
      CaseOutstanding: [10×1 double]

Use ibnr to compute IBNR reported claims for a bornhuetterFerguson object.

ibnrClaims = ibnr(bf,"reported")

ibnrClaims = 10×1
103 ×

         0
    0.0052
    0.0167
    0.0347
    0.0572
    0.0889
    0.1496
    0.3006
    0.6118
    1.5509

Input Arguments

bf — Bornhuetter-Ferguson

bornhuetterFerguson object

Bornhuetter-Ferguson object, specified as a previously created bornhuetterFerguson object.

Data Types: object

referenceClaimsType — Type of claims data

'reported' (default) | character vector with value 'reported' or 'paid' | string with value "reported" or "paid"

Type of claims data, specified as a character vector or a string.

Data Types: char | string

Output Arguments

ibnrClaims — IBNR claims

array

IBNR claims, returned as an array.

More About

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.

Version History

Introduced in R2020b