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Gunnar Andersson, 2008-06-13

Biometric assumptions in life insurance with focus on the Swedish market, recent development

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References

Parts of the work below has been carried out and under work by different working parties within the Swedish Research Council for Actuarial Science(Erik Alm, Gunnar Andersson, Bengt von Bahr, Åsa Larson, Jörgen Olsén (part of the work), Ellinor Samuelsson, Christian Salmeron and Arne Sandstöm)

In principal all calculations are carried out by Ellinor Samuelsson and the major part of the text in the reports is written by Gunnar Andersson and Ellinor Samuelsson

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1. Introduction2. Legal status regarding uni-sex (and age?)

a. EG-directive (2004/113/EEG)b. Swedish legislation: FFS 2004/05:147c. Agreement with Swedish industry

3. New assumptions for mortality4. Disability

a. Occurenceb. t-frequenciesc. Terminating

Agenda

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Folksam – that’s us!• Folksam is a mutual company

working with (in principal) all lines of business within insurance

• Our customers are also our owners

• Our profit doesn’t go to share-holders, it stays within the company and benefits us all

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Short Facts about Folksam 2007-12-31

• Folksam was founded in 1908

• We have about 4 million customers (cf Swedens pop. 9 mill people)

• We have SEK 20,3 billion Swedish crowns in written premiums

• We settle 600 000 claims every year

• We manage about SEK 270 billion Swedish crowns in assets

• We are 3 700 employees, 51 % women and 49 % men

• We have 80 offices throughout the country

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The Folksam story

1908

The mutual fire insurance co-operative (Samarbete) is established

1914

The life insurance company (Folket) is established

1925

The two lines of business begin co-ordinating

1946The name Folksam, a combination of Folket and Samarbete, is introduced

2008

Folksam celebrates 100 years

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1. Introduction2. Legal status regarding uni-sex (and age?)

a. EG-directive (2004/113/EEG)b. Swedish legislation: FFS 2004/05:147c. Agreement with Swedish industry

3. New assumptions for mortality4. Disability

a. Occurenceb. t-frequenciesc. Terminating

Agenda

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Basicly there are three objectives for mortality investigations:

1. The first objective is to keep track of the rate of mortality for reserving purposes.2. The second objective is to fulfill demands for a

sound insurance business; i.e. having a ”solid” capitalisation of the operation. More known today in the industry as fulfilling the forthcoming rules for Solvency II (in place 2012?; compare Basel II for banks).

3. The third objective is accounting and transparancy purposes.

Objectives

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Another, and more recent adressed objective (andmaybe even the most important one) is to, using legislation, get rid of unequal treatment due to (for instance) sex.

This applies to thepricing of insuranceproducts as well.

In the furure, age might be treated inthe same way.

Gender-dependence in pricing of products

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More examples:

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1. There is an agreement signed by Finansinspektionen (the Swedish Supervisning Authority), Försäkringsförbundet (the Swedish Insurance Federation) and Konsumenternas Försäkringsbyrå (KFB, the Swedish Consumers Insurance Bureau) that ”proof” of need for gender-dependence in premium calculations, shall be published by KFB.

2. The study shall be carried out by Försäkringstekniska Forskningsnämnden (FTN, the Swedish Research Council for Actuarial Science).

Objectives

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1. Lines of business in focus are life, disability, accident and motor insurance.

2. Actions taken:1. Life; performed once (publ. 2007)2. Disability; on its way (publ. 2009?)3. Accident; decided not to carry out investigation4. Motor; on its way (publ. 2008)

Objectives

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1. Introduction2. Legal status regarding uni-sex (and age?)

a. EG-directive (2004/113/EEG)b. Swedish legislation: FFS 2004/05:147c. Agreement with Swedish industry

3. New assumptions for mortality4. Disability

a. Occurenceb. t-frequenciesc. Terminating

Agenda

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Illustration

Simple model:

where is the rate of mortality (cf qx.)

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Lifelength (mortality) investigations

1. SCB is carrying out investigations every year2. Most insurance companies have to few

observations for carrying out acceptable stydies3. We estimate q/4. Smoothing of using relevant analytical formula,

very common in the nordic countries, Makehams formula.

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M90

1. M90 carried out in the late 1988-89

2. α = 0.0013. β = 0.0000124. γ = 0.101314

six years time difference between men and females.

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M90

Drawbacks with M90:

• The main problem is that it does not take the time trend into consideration

• Bad for low ages• Bad for high ages; one suggested adjustment:

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Expected remaining lifelength

M90 – expected remaining lifelength

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Lee-Carter

1. More complex statistical work2. Introduces a time trend – population (SCB)3. Estimation of q/4. Major problem in practise: Insurance companies

(in Sweden) can not handle other models than Makeham. The cost for introducing a full Lee-Carter model is probably somewhere between 50-100 MSEK for the Swedish insurance industry.

5. Solution: Makeham models for different co-horts, see for example:

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Makeham for separate co-horts

Expected remaining life length at age 65:

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Lee-Carter model

Introducing a time trend is done in the following way:

Estimating parameters is done by a using a Poisson- likelihood model:

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Parameter interpretion in the model

• The alpha-term can be treated as the general shape of the mortality

• The kappa-factor is the time-trend in the mortality

• The beta-factor represents the age-specific impact of the time trend

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Overall result

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Kappa-parameter

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Beta-parameter

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Expected remaining life length at age 65 - population

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1. Introduction2. Legal status regarding uni-sex (and age?)

a. EG-directive (2004/113/EEG)b. Swedish legislation: FFS 2004/05:147c. Agreement with Swedish industry

3. New assumptions for mortality4. Disability

a. Occurenceb. t-frequenciesc. Terminating

Agenda

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Layout of disability investigation

• Most insurance companies (in Sweden) have difficulties in arriving in sound estimates of disabilityreserves mainly because of small portfolios.

• Also, the length of time as disabled is extremelyimportant for the finances of the company.

• Due to above mentioned legal considerationsthe insurance industry needs to verify that gender is an important parameter in designing disability products.

• Investigation is carried out by FTN 2008 - ?• Results will be common for the whole industry with

”portfolio”-adjustments• Not completely clear regarding data structure• Will be published by KFB

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Content of study

• Standard for reporting data is (in principal) decided in co-operation with the industry

• Model-research is on its way (international methodsare considered)

• Swedish population will probably be used as reference

• Results will be valid for different kinds of disability insurance

• Questions are raised from some companies regarding publicity

• Data gathering will start during summer 2008

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Illustration

Simple model:

(intensity)

(probability)

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Notation

• ν(x) = the disability intensity

• λ(x,t) = the probability that a person who falls ill at age x remains ill t years later

• ξ(x,t) = ν(x) λ(x,t) dx is the probability of falling ill and remaining disabled

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Miscellaneous

• Works well with a semi-Markov approach (time dependence when entering a new state)

• Model depends in practise very often on availability of accurate data

• Political risks can influence the quality of data

• Data are highly correlated with unemployment pattern

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Estimating parameters - occurence

• Irregular in time, i.e. changes in peoples behaviour which can influence time trends

• Occurence is estimated by taking the ratio between number of occurences and population

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t-frequences

• ξ(x,t) is by definition equal to the probability that an(well) individual get disabled and t years later still is disabled

• In some situations data records does not consist of more information than what is needed to estimatethese probabilities

• These estimates are called t-frequences

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Estimation termination function

1. Kaplan-Meier estimator; • product-limit estimator• survival functions

2. Nelson-Aalen technique; • based on counting process• martingale technique

3. Statistical properties are well established for both techniques

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Smoothing terminating function

The Swedish technique has been, through decades,to apply a sum of exponential expressions to the estimated terminating function, each part taking care of different parts of the sick period.

(Age when getting sick is x and time as sick is denoted t).

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Nonparametric approach

• If one decides not to use a parametric function one can consider a matrix approach.

• Size of matrix will create some difficulties even though it can be taken care of.

• Classification of time and age will be crucial for size of matrix.

Thank you!