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ultimateClaims

Compute projected ultimate claims for capeCod object

Description

example

projectedUltimateClaims = ultimateClaims(cc) computes the projected ultimate claims for each origin period, based on the earned premium and the selected claims ratios for a capeCod object.

Examples

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This example shows how to compute the projected ultimate claims for a capeCod object for 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: {10x1 cell}
                     Development: {10x1 cell}
                          Claims: [10x10 double]
                  LatestDiagonal: [10x1 double]
                     Description: ""
                      TailFactor: 1
    CumulativeDevelopmentFactors: [1.3069 1.1107 1.0516 1.0261 1.0152 ... ]
               SelectedLinkRatio: [1.1767 1.0563 1.0249 1.0107 1.0054 ... ]

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: [2.4388 1.4070 1.1799 1.0810 1.0378 ... ]
               SelectedLinkRatio: [1.7333 1.1925 1.0914 1.0417 1.0196 ... ]

Create a capeCod object where the first input argument is the reported development triangle, the second input argument is the paid development triangle, and the third input is the earned premium.

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

           ReportedTriangle: [1x1 developmentTriangle]
               PaidTriangle: [1x1 developmentTriangle]
              EarnedPremium: [10x1 double]
              UsedUpPremium: [10x1 double]
       EstimatedClaimRatios: [10x1 double]
         ExpectedClaimRatio: 0.4258
    EstimatedExpectedClaims: [10x1 double]
          PercentUnreported: [10x1 double]
            CaseOutstanding: [10x1 double]

Use ultimateClaims to compute the projected ultimate claims.

projectedUltimateClaims = ultimateClaims(cc)
projectedUltimateClaims = 10×1
103 ×

    5.0894
    5.1876
    5.6382
    5.8520
    5.9447
    5.8367
    5.8332
    6.0632
    6.0893
    5.9459

Input Arguments

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Cape Cod object, specified as a previously created capeCod object.

Data Types: object

Output Arguments

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Projected ultimate claims obtained using the Cape Cod technique, returned as a vector.

More About

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Ultimate Claims

Ultimate claims are the total sum the insured, its insurer, and/or its reinsurer pay for a fully developed loss. A fully developed loss is the paid losses plus outstanding reported losses and incurred-but-not-reported (IBNR) losses.

Knowing the exact value of ultimate losses might not be possible for a long time after the end of a policy period. Actuaries assist with these projections for purposes of financial modeling and year-end reserve determinations.

Version History

Introduced in R2021a