ultimateClaims

Compute projected ultimate claims for bornhuetterFerguson object

Syntax

projectedUltimateClaims = ultimateClaims(bf)

projectedUltimateClaims = ultimateClaims(___,referenceClaimsType)

Description

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

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

Examples

Compute Projected Ultimate Claims for bornhuetterFerguson Object

This example shows how to compute the projected ultimate claims for a bornhuetterFerguson 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: {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, case outstanding, IBNR, 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 ultimateClaims to compute the projected ultimate claims for each origin period, based on the earned premium and the selected claims ratios.

projectedUltimateClaims = ultimateClaims(bf,"reported")

projectedUltimateClaims = 10×1
103 ×

    5.0894
    5.1851
    5.6421
    5.8384
    5.9358
    5.8617
    5.8639
    6.1550
    6.1069
    6.4968

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"

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

Data Types: char | string

Output Arguments

projectedUltimateClaims — Projected ultimate claims obtained using Bornhuetter-Ferguson technique

vector

Projected ultimate claims obtained using the Bornhuetter-Ferguson technique, returned as a vector.

More About

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 R2020b