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MTPL as a challenge to actuaries PowerPoint PPT Presentation

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

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

• 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 2 (“realistic”):

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