Compute CDFs to ultimate claims for developmentTriangle
object
selectedLinkRatiosTable = cdfSummary(developmentTriangle)
Calculate the CDFs and the percentage of total claims for a developmentTriangle object using 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: [1x10 double]
SelectedLinkRatio: [1x9 double]
Use linkRatioAverages function to calculate the different link ratio averages.
LinkRatioAveragesTable = linkRatioAverages(dT)
LinkRatioAveragesTable=8×9 table
12-24 24-36 36-48 48-60 60-72 72-84 84-96 96-108 108-120
______ ______ ______ ______ ______ ______ _____ ______ _______
Simple Average 1.1767 1.0563 1.0249 1.0107 1.0054 1.0038 1.003 1.002 1.001
Simple Average - Latest 5 1.172 1.056 1.0268 1.0108 1.0054 1.0038 1.003 1.002 1.001
Simple Average - Latest 3 1.17 1.0533 1.027 1.0117 1.0057 1.0037 1.003 1.002 1.001
Medial Average - Latest 5x1 1.1733 1.0567 1.0267 1.0103 1.005 1.004 1.003 1.002 1.001
Volume-weighted Average 1.1766 1.0563 1.025 1.0107 1.0054 1.0038 1.003 1.002 1.001
Volume-weighted Average - Latest 5 1.172 1.056 1.0268 1.0108 1.0054 1.0038 1.003 1.002 1.001
Volume-weighted Average - Latest 3 1.1701 1.0534 1.027 1.0117 1.0057 1.0037 1.003 1.002 1.001
Geometric Average - Latest 4 1.17 1.055 1.0267 1.011 1.0055 1.0037 1.003 1.002 1.001
Use the cdfSummary function to calculate CDFs and the percentage of total claims and return a table with the selected link ratios, CDFs, and percent 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
developmentTriangle — Development triangledevelopmentTriangle objectDevelopment triangle, specified as a previously created developmentTriangle object.
Data Types: object
selectedLinkRatiosTable — CDF to ultimate claimsCDF to ultimate claims, returned as a table. The table shows the selected ratios, CDFs, and percentage of total claims.
Calculating the cumulative development factors (CDFs) of a random variable is a method to describe the distribution of random variables.
The CDF of a real-valued random variable X, or just distribution function of X, evaluated at x, is the probability that X takes a value less than or equal to x.
Ultimate claims are the total sum the insured, its insurer(s), and/or its reinsurer(s) pay for a fully developed loss. A fully developed loss is the paid losses plus outstanding and reported losses and incurred-but-not-reported (IBNR) losses.
claimsPlot | fullTriangle | linkRatioAverages | linkRatios | linkRatiosPlot | ultimateClaims | view
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