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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

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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 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 income5
Reserving large BI claims – loss of income

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

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

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