Mtpl as a challenge to actuaries
This presentation is the property of its rightful owner.
Sponsored Links
1 / 27

MTPL as a challenge to actuaries PowerPoint PPT Presentation


  • 100 Views
  • Uploaded on
  • Presentation posted in: General

MTPL as a challenge to actuaries. HOT TOPICS of MTPL from the perspective of a Czech actuary. Contents. Dynamism and stochasticity of loss reserving methods Regression methods Bootstrapping Appropriate reserving of large bodily injury claims Practical implications of segmentation

Download Presentation

MTPL as a challenge to actuaries

An Image/Link below is provided (as is) to download presentation

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.


- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -

Presentation Transcript


Mtpl as a challenge to actuaries

MTPL as a challenge to actuaries

HOT TOPICS of MTPL from the perspective of a Czech actuary


Contents

Contents

  • Dynamism and stochasticity of loss reserving methods

    • Regression methods

    • Bootstrapping

  • Appropriate reserving of large bodily injury claims

  • Practical implications of segmentation

    • Simultaneous co-existence of different rating factors on one market

    • Price sensitivity of Czech MTPL policy holders


R eserving methods for mtpl

Reserving methods for MTPL

Problems:

  • demonopolisation

    • new players on the market

      • not optimal claims handling (training of loss adjusters, upgrading SW)

         development factors are unstable

  • guarantee fund (GF)

    • settlement of claims caused by

      • uninsured drivers

      • unknown drivers

        • unknown exposition + GF=new(unknown) entity within the system

          • unstable development factors

          • significant trend in incurred claims

  • REQUIRE: incorporation of stochasticity and dynamism into methods


R eserving methods for mtpl1

Reserving methods for MTPL

Stochasticity:

  • “easy” but reasonable way = bootstrap

    • fitting a preferred projection method to a data triangle

    • comparison of original data and projection  residuals

    • sampling residuals and generation of many data triangles

    • derivation of ultimates from these sampled triangles

    • statistical analysis of ultimates/IBNRs/RBNSes:

      • expected value

      • standard error

      • higher moments

      • distribution


R eserving methods for mtpl2

Reserving methods for MTPL

Dynamism:

  • regression methods - a natural extension of Chain-ladder

    Y(i,j)=b*Y(i,j-1)+e(i), Var(e)=2Y(i,j-1)

    • special cases:

      =1 (chain-ladder)

      =2 

      =0 (ordinary least sq. regression)

  • extension: Y(i,j)=a0+a1*i+b*Y(i,j-1)+e(i), Var(e)=2Y(i,j-1)

    = extended link ratio family of regression models described by

    G.Barnett & B. Zehnwirth (1999)


  • R eserving methods for mtpl3

    Reserving methods for MTPL

    Modelling trends in each “direction”:

    • accident year direction

      • in case of adjustment for exposure  probably little changes over time

      • in case of unavailability of exposure  very important

    • development year direction

    • payment year direction

      • gives the answer for “inflation”

        • if data is adjusted by inflation, this trend can extract implied social inflation

    • MODEL:

      development years j=0,…,s-1; accident years i=1,…,s; payment years t=1,…,s

      = probabilistic trend family (G.Barnett & B. Zehnwirth (1999))


    R eserving methods for mtpl example

    Reserving methods for MTPL - example

    Construction of PTF model using STATISTICA (data analysis software system)

    • Data set

      • claim numbers caused by uninsured drivers in Czech Republic 2000-2003

      • triangle with quarterly origin and development periods

    • Exposure – unknown

    • Full model:

      • applied on Ln(Y)

      • 46 parameters


    R eserving methods for mtpl example1

    Reserving methods for MTPL - example

    Complete design matrix

    • necessary to exclude intercept

    • too many parameters

      necessary to create submodel

      GOAL: description of trends within 3 directions

      and changes in these trends

      optimal submodels = submodels adding together columns (“columns-sum submodels (CSS)”)

    • How to create submodels:

      • manually

      • use forward stepwise method

        • it is necessary to transform final model into CSS submodel, this model will still have too many parameters (problem of multi-colinearity + bad predictive power)

        • necessity of subsequent reduction of parameters


    R eserving methods for mtpl example2

    Reserving methods for MTPL - example

    • usually possible to assume  model with intercept

    • final model for Czech guarantee fund:

      • 7 parameters

      • R2=91%

      • tests of normality of standardized residuals

      • autocorrelation of residuals rejected


    R eserving methods for mtpl example3

    Reserving methods for MTPL - example


    R eserving methods for mtpl example4

    Reserving methods for MTPL - example


    R eserving methods for mtpl example5

    Reserving methods for MTPL - example

    Statistics of total ultimate for 2000-3

    • bootstrap method based upon assumptions of regression model

      • predict future values (i+j>16)  mean,quantiles  st. dev.

      • bootstrap future data (assumption of normality)

      • descriptive statistics based upon bootstrapped samples


    R eserving methods for mtpl4

    Reserving methods for MTPL

    Conclusions:

    • we got a reasonable model using PTF model for describing and predicting incurred claims of guarantee fund

    • model reasonably describes observed trend in data and solves the problem of non-existence of exposure measure


    Reserving large bodily injury claims

    Reserving large bodily injury claims

    • Importance of properly reserving large bodily injury (BI) claims

    • Mortality of disabled people

    • Sensitivity of reserve for large BI claim upon estimation of long term inflation/valorization processes


    Reserving large bi claims importance

    Reserving large BI claims - importance

    • More than 90% of large claims consists from large BI claims

    • Proportion of large BI claims on all MTPL claims measured relatively against:

      • number of all claims

      • amount of all claims

    • Decreasing trend is only due to:

      • long latency of reporting BI claims to insurer

      • not the best reserving practice.

    • It’s reasonable to assume that share of BI claims is aprox. 20%.


    Reserving large bi claims importance1

    Reserving large BI claims - importance

    • Due to the extreme character of large BI claims the importance of appropriate reserving is inversely proportional to the size of portfolio

       Example: proportion of large BI claims on all claims of Czech Insurers Bureau („market share“ approx. 3%)


    Reserving large bi claims mortality

    Reserving large BI claims - mortality

    • Classification of disabled people

       criteria:

      • seriousness

        • partial disability

        • complete disability

    • main cause

      • illness

      • injury =traffic accidents, industrial accidents,...

  • Availability of corresponding mortality tables in Czech Republic


  • Reserving large bi claims mortality1

    Reserving large BI claims - mortality

    • Comparison of mortality of regular and disabled people

    It’s reasonable to assume that „illness“ disability implies higher

    mortality than “accident” disability  proper reserve is probably


    Reserving large bi claims types of damage

    Reserving large BI claims – types of damage

    • No problem:

      • Pain and suffering

      • Loss of social status

    • Problem

      • Home assistance (nurse, housmaid, gardner, ...)

        depends upon:

        • mortality

        • future development of disability

    • Loss of income

      depends upon:

      • mortality

      • future development of disability

      • structure of future income  prediction of long term inflation and valorization


    Reserving large bi claims loss of income

    Reserving large BI claims – loss of income

    Loss of income in Czech Republic

    = “valorized income before accident”

    - “actual pension”

    • “actual income (partially disabled)”

      Needs:

  • estimate of future valorization of incomes... vI(t)

  • estimate of future valorization of pensions... vP(t)

    • both depend upon economic and political factors

  • estimate of future inflation of incomes... ii(t)

    • depends upon economic factors


  • Reserving large bi claims loss of income1

    Reserving large BI claims – loss of income

    Notation:

    • income before accident ... IB

    • pension ... P

    • income after accident ... IA

    • vI(t), vP(t), ii(t)

    • inflation ... i (used for discounting future payments)

    • Small differences among vI(t), vP(t), ii(t) andi can imply dramatic changes in needed reserve

       Proportion of IB , P and IA is crucial

      Assumptions:

    • dependence upon mortality is not considered

    • complete disability  IA=0

    • vI(t), vP(t) and ii(t) are constant over time


    Reserving large bi claims loss of income2

    Reserving large BI claims – loss of income

    Examle 1:

    • income before accident ... IB = 10 000 CZK

    • pension ... P = 6 709 CZK

    • initial payment of ins. company = 3 291 CZK

    • vI(t)=3%

    • vP(t)=2%

    • i = 4%

    • expected interest rate realized on assets of company is higher than both valorizations

      Question:

    • Will the payments of ins. company increase faster or slower than interest rate?


    Reserving large bi claims loss of income3

    Reserving large BI claims – loss of income


    Reserving large bi claims loss of income4

    Reserving large BI claims – loss of income

    Examle 2 (“realistic”):


    Reserving large bi claims loss of income5

    Reserving large BI claims – loss of income

    Examle 3 (“a blessing in disguise”) – degressive pension system


    Segmentation problem of asymmetric information

    Segmentation–problem of asymmetric information


    Segmentation problem of asymmetric information1

    Segmentation – problem of asymmetric information

    During 2000-2003:

    • identical rating factors used by all insurers

    • partial regulation of premium

    • real spread of premium +/- 5% within given tariff category

      annual fluctuation of policyholders

      = more than 5% of all registered vehicles

      From the beginning of 2004:

    • beginning of segmentation

      • the difference in premium level applied by different insurers >10% holds for a large set of policyholders

         probability of loss due to assymetric information grows


  • Login