MTPL as a challenge to actuaries

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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

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
• Simultaneous co-existence of different rating factors on one market
• Price sensitivity of Czech MTPL policy holders
Reserving methods for MTPL

Problems:

• demonopolisation
• new players on the market

 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
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
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:

=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)

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))

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
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
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
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
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
• 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
• 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 - 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
• 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 - 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
• 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

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 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 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 income

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

Segmentation – problem of asymmetric information

During 2000-2003:

• identical rating factors used by all insurers