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Individual Claim Development An Application

Explore an alternative reserving method for motor liability claims using the Deterministic Individual Claim Development (ICD) methodology. This method estimates future claim payments based on historical individual incremental claim payments, without aggregating the data.

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Individual Claim Development An Application

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  1. Individual Claim DevelopmentAn Application Bas Lodder 9 March 2015

  2. Chain LadderBasedMethodsLimitations • Classicalchainladder (CL) basedclaimreservingmethodsarestandardpracticefor • attritionalclaims • large volumes • historicallyhomogeneousrisks • claimswithexpecteddevelopmentbased on AY / DY only (nocalendaryeareffect) • sufficienthistoricalclaimsinformation • Counterexample: motorliability • includes large claims • claiminflationeffects • propertydamage vs. bodilyinjury general non-homogeneity • changes in legal environment (whiplash, „Via sicura“)  historical non-homogeneity • lump-sumandannuitypayments  shocks, complextailbehaviour Weneedto find an alternative reservingmethodformotorliabilityclaims Individual Claim Development - Bas Lodder, 09/03/2015

  3. Alternative Claim ReservingMethodsIndividual Claim Development • Classical CL methodsaggregatehistoricalclaimpayments per risk in an AY – DY triangle • Can weimproveourestimatesifweskiptheaggregationstep? • Option 1: deterministic individual claimdevelopment • triangulation: similartoclassical CL methods • bestestimatebynearestneighbourapproach • Option 2: stochastic individual claimdevelopment • triangulation: developmentpatternbased on numberofpayments per claim • stochasticsimulationoffuturepayments (frequencyandseverity) • literature: Antonio et al. (2012), Pigeon et al. (2013), Pigeon et al. (2014) • Weneed a secondopinionforour CL bestestimate Chosen method: deterministic individual claimdevelopment Individual Claim Development - Bas Lodder, 09/03/2015

  4. Deterministic Individual Claims Development (ICD) Methodology • Givenhistorical individual incrementalclaimpaymentsCi,k, weneedtoestimatefutureclaimpaymentsĈi,kforeachclaimiandeach DY k ≤ kmax = maxk(Ci,k) • Ĉi,k = αi,k * Σj: AY(j) + k ≤ CY((Di,j)β * Cj,k), with • Di,j = distancemeasurebased on historicalclaimdevelopmentdifference • αi,k= 1 / (Σj: AY(j) + k ≤ CY((Di,j)β ) (scalefactor) • βϵ (-∞, 0) (shapefactor) • Options forcalculatingDi,j • claimsbasis: paidorincurred • method: additive ormultiplicative • differences: absolute orsquared k (DY) Ci,k AY, i CY Ĉi,k Individual Claim Development - Bas Lodder, 09/03/2015

  5. Deterministic Individual Claims Development (ICD) Example • First wecalculatethedistancesDi,j: • D3,1 = │C3,0 - C1,0│ + │C3,1 - C1,1│ = │10 - 40│ + │40 - 80│ = 70 • Similarly, we find D3,2 = 30, D4,1 = 20, D4,2 = 20 andD4,3 = 10 • Next, wecalculatethescalingfactorsαi,k, with, say, β = -1 andβ = -2 • β = -1: α3,2 = 1 / (1/D3,1 + 1/D3,2) = 1 / (1/70 + 1/30) = 21 • β = -2: α3,2 = 1 / (1/(D3,1)2 + 1/(D3,2)2) = 1 / (1/4900 + 1/900) = 44100 / 58 ≈ 760 • Similarly, we find α4,1 = 5 resp. 66.7 andα4,2 = 10 resp. 200 • Now, wederivetheexpectedclaimpaymentsĈi,k(forsakeofsimplicity, wetakeβ = -1) • Ĉ3,2 = α3,2 * (C1,2/D3,1 + C2,2/D3,2) = 21 * (0/70 + 40/30) = 28 • Ĉ4,1 = α4,1 * (C1,1/D4,1 + C2,1/D4,2 + C3,1/D4,3) = 5 * (80/20 + 60/20 + 40/10) = 55 • Ĉ4,2 = α4,2 * (C1,2/D4,1 + C2,2/D4,2) = 10 * (0/20 + 40/20) = 20 28 55 20 Di,jisconstant in k, αi,kis not! Individual Claim Development - Bas Lodder, 09/03/2015

  6. ICD: An ApplicationProcess, Data, Assumptions • Model implementationwith Frank Cuypers and Simone Dalessi, Prime Re Services • methodology • VBA-based Excel template • testingloops • Data andassumptions in thispresentation • inputdata: large (0.2 – 1.0 MCHF) andmid-size (0.1 – 0.2 MCHF) Swiss Mobiliar motorliabilityclaims • claimsbasis: paid • method: additive • differences: absolute • β = -2, i.e. Ĉi,k = αi,k * Σj: AY(j) + k ≤ CY((Di,j)-2 * Cj,k) Individual Claim Development - Bas Lodder, 09/03/2015

  7. Mid-sizeclaims – Actual vs. Expected, CY 2014500 claims • Althoughclaimamountsvaryby AY, both CL and ICD estimatesseemtobequiteaccurate Individual Claim Development - Bas Lodder, 09/03/2015

  8. Mid-sizeclaims – Estimation Error, CY 2014500 claims • Large historicalsingleclaimpaymentscauseoverestimation in AYs 2002-2004 • ICD outperforms CL in these AYs sinceitputsnegligibleweight on theclaimforwhichthesepaymentsweremade • Other claimdevelopmentscausesimilarestimationerrorstobothmethods Individual Claim Development - Bas Lodder, 09/03/2015

  9. Mid-sizeclaims – Actual vs. Expected, CY 201460 claims • Werandomlypicked 4 claims per AY toreducethenumberofclaims • The smallernumberofclaimscausesshocks in claimpayments • The shock in AY 2004 was knownby CY 2011, theone in AY 2008 camelater Individual Claim Development - Bas Lodder, 09/03/2015

  10. Mid-sizeclaims – Estimation Error, CY 2014 60 claims • Due tothesmallernumberofclaims, deviationsfromactualpaidamountsare larger • In particular, thepayment in DY 5 of AY 2008 cameunexpected • Contrarytoouroverallexpectationofsmallerdatasets, ICD does not significantlyoutperform CL in thisexample, exceptfor AYs 2009 and 2010 Individual Claim Development - Bas Lodder, 09/03/2015

  11. Large claims – Actual vs. Expected, CY 20141‘600 claims • The declinepaidclaimamountsiscausedby • Decline in whiplashclaims • Difference in claimmaturity Individual Claim Development - Bas Lodder, 09/03/2015

  12. Large claims – Estimation Error, CY 20141‘600 claims • The decline in whiplashclaimscauses large estimationerrors in bothmethods • Otherwise, ICD performsslightlybetterhere Individual Claim Development - Bas Lodder, 09/03/2015

  13. Large claims – Actual vs. Expected, CY 201460 claims • The decline in claimspaymentsover time ismostlycausedbyfrequencyandthereforethereduceddataset (4 claims per AY) is not affected Individual Claim Development - Bas Lodder, 09/03/2015

  14. Large claims – Estimation Error, CY 201460 claims • As expected, thereductionofclaimscauses larger estimationerrors • ICD still performsslightlybetterthan CL Individual Claim Development - Bas Lodder, 09/03/2015

  15. ICD: An ApplicationConclusions • Fortheexamplesshown, ICD seemstobeat least asgood a methodas CL • ICD outperforms CL if large claimswithunusualpatternsareincluded in claimshistory • Performance does not seemtodepend on volume • Nooutperformanceifclaimshistorycontainssignificantcalendaryeareffects (changes in legal environment, inflation) orchanges in claimshandlingspeed Individual Claim Development - Bas Lodder, 09/03/2015

  16. Micro-Level ReservingWhy (not)? • Deterministic ICD canperform well ifclaimsdata do not containcalendareffects • Challenges • IBNYR claimsneedtobeestimatedseparately – comparisonwith CL onlypossible after removing IBNYR claims • a large amountof individual claimsdataneedstobeprocessed IT / actuarialtools • the model presentedprovides a bestestimate, errorestimatescanbederivedas well • Likeanyclaimsreservingmethod, ICD requiresactuarialjudgement! • ensuringhomogeneity in claimshistory • parameterchoice / model options • sensitivitytesting – robustness! • understandingdifferencesto CL andothermodels • Outlook: stochastic ICD • moresuitable in caseofchangingclaimshandlingspeed • canprovide a distributionofultimateclaimamounts Individual Claim Development - Bas Lodder, 09/03/2015

  17. ICD: An ApplicationFurther questions ? Individual Claim Development - Bas Lodder, 09/03/2015

  18. Dessert: Personal Liability (0.1 MCHF – 5 MCHF)Incurreddata(300 claims) • Thisdatasetcontainssome large all-or-nothingclaims, mostly in earlier AYs • In CL, such claimsaffectage-to-agefactors, causinglowestimates • In ICD, such claims will obtainnegligibleweights • The overall negative deviationis due to a combinationof • conservativeclaimreserves • fastersettlementofclaimsover time Individual Claim Development - Bas Lodder, 09/03/2015

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