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fullTriangle

Display full development triangle including ultimate claims

Description

example

fullTriangleTable = fullTriangle(developmentTriangle) calculates the projected claims for every origin and development period in the lower half of the development triangle.

Examples

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Calculate the projected claims for every origin and development period in the lower half of the development triangle for a developmentTriangle 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.

dT = developmentTriangle(data)
dT = 
  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 ... ]

Use the ultimateClaims function to calculate CDFs and the percentage of total claims and return a table with the selected link ratios, CDFs, and percentage of total claims.

dT.SelectedLinkRatio = [1.1755, 1.0577, 1.0273, 1.0104, 1.0044, 1.0026, 1.0016, 1.0006, 1.0004];
selectedLinkRatiosTable = cdfSummary(dT)
selectedLinkRatiosTable=3×10 table
                                12-24      24-36      36-48      48-60      60-72      72-84     84-96     96-108    108-120    Ultimate
                               _______    _______    _______    _______    _______    _______    ______    ______    _______    ________

    Selected                    1.1755     1.0577     1.0273     1.0104     1.0044     1.0026    1.0016    1.0006    1.0004        1    
    CDF to Ultimate              1.303     1.1084      1.048     1.0201     1.0096     1.0052    1.0026     1.001    1.0004        1    
    Percent of Total Claims    0.76747    0.90216    0.95422    0.98027    0.99046    0.99482    0.9974     0.999    0.9996        1    

Use the fullTriangle function to create a table containing the filled development triangle.

fullTriangleTable = fullTriangle(dT)
fullTriangleTable=10×11 table
              12        24        36        48        60        72        84        96       108       120      Ultimate
            ______    ______    ______    ______    ______    ______    ______    ______    ______    ______    ________

    2010    3995.7      4635    4866.8    4964.1    5013.7    5038.8      5059    5074.1    5084.3    5089.4     5089.4 
    2011      3968    4682.3    4963.2    5062.5    5113.1    5138.7    5154.1    5169.6    5179.9      5182       5182 
    2012      4217    5060.4      5364    5508.9    5558.4    5586.2    5608.6    5625.4    5628.8      5631       5631 
    2013    4374.2    5205.3    5517.7    5661.1    5740.4    5780.6    5803.7      5813    5816.5    5818.8     5818.8 
    2014    4499.7    5309.6    5628.2    5785.8    5849.4    5878.7      5894    5903.4    5906.9    5909.3     5909.3 
    2015    4530.2    5300.4    5565.4    5715.7    5772.8    5798.2    5813.3    5822.6    5826.1    5828.4     5828.4 
    2016    4572.6    5304.2    5569.5    5714.3    5773.7    5799.1    5814.2    5823.5      5827    5829.3     5829.3 
    2017    4680.6    5523.1    5854.4    6014.3    6076.8    6103.6    6119.4    6129.2    6132.9    6135.3     6135.3 
    2018    4696.7    5495.1    5812.2    5970.9    6032.9    6059.5    6075.2      6085    6088.6    6091.1     6091.1 
    2019    4945.9    5813.9    6149.4    6317.2    6382.9      6411    6427.7      6438    6441.8    6444.4     6444.4 

Input Arguments

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Development triangle, specified as a previously created developmentTriangle object.

Data Types: object

Output Arguments

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Filled development triangle, returned as a table.

Introduced in R2020b