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

1. Gunnar Andersson, 2008-06-13 Biometric assumptions in life insurance with focus on the Swedish market, recent development

2. 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

3. Agenda • Introduction • Legal status regarding uni-sex (and age?) • EG-directive (2004/113/EEG) • Swedish legislation: FFS 2004/05:147 • Agreement with Swedish industry • New assumptions for mortality • Disability • Occurence • t-frequencies • Terminating

4. 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

5. 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

6. 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 1946 The name Folksam, a combination of Folket and Samarbete, is introduced 2008 Folksam celebrates 100 years

7. Agenda • Introduction • Legal status regarding uni-sex (and age?) • EG-directive (2004/113/EEG) • Swedish legislation: FFS 2004/05:147 • Agreement with Swedish industry • New assumptions for mortality • Disability • Occurence • t-frequencies • Terminating

8. Objectives • Basicly there are three objectives for mortality investigations: • 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.

9. Gender-dependence in pricing of products Another, and more recent adressed objective (and maybe even the most important one) is to, using legislation, get rid of unequal treatment due to (for instance) sex. This applies to the pricing of insurance products as well. In the furure, age might be treated in the same way.

10. More examples:

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

12. Objectives • Lines of business in focus are life, disability, accident and motor insurance. • Actions taken: • Life; performed once (publ. 2007) • Disability; on its way (publ. 2009?) • Accident; decided not to carry out investigation • Motor; on its way (publ. 2008)

13. Agenda • Introduction • Legal status regarding uni-sex (and age?) • EG-directive (2004/113/EEG) • Swedish legislation: FFS 2004/05:147 • Agreement with Swedish industry • New assumptions for mortality • Disability • Occurence • t-frequencies • Terminating

14. Illustration Simple model: where  is the rate of mortality (cf qx.)

15. Lifelength (mortality) investigations • SCB is carrying out investigations every year • Most insurance companies have to few observations for carrying out acceptable stydies • We estimate q/ • Smoothing of  using relevant analytical formula, very common in the nordic countries, Makehams formula.

16. M90 • M90 carried out in the late 1988-89 • α = 0.001 • β = 0.000012 • γ = 0.101314 • six years time difference between men and females.

17. 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:

18. Expected remaining lifelength M90 – expected remaining lifelength

19. Lee-Carter • More complex statistical work • Introduces a time trend – population (SCB) • Estimation of q/ • 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. • Solution: Makeham models for different co-horts, see for example:

20. Makeham for separate co-horts Expected remaining life length at age 65:

21. Lee-Carter model Introducing a time trend is done in the following way: Estimating parameters is done by a using a Poisson- likelihood model:

22. 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

23. Overall result

24. Kappa-parameter

25. Beta-parameter

26. Expected remaining life length at age 65 - population

27. Agenda • Introduction • Legal status regarding uni-sex (and age?) • EG-directive (2004/113/EEG) • Swedish legislation: FFS 2004/05:147 • Agreement with Swedish industry • New assumptions for mortality • Disability • Occurence • t-frequencies • Terminating

28. Layout of disability investigation • Most insurance companies (in Sweden) have • difficulties in arriving in sound estimates of disability • reserves mainly because of small portfolios. • Also, the length of time as disabled is extremely • important for the finances of the company. • Due to above mentioned legal considerations • the 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

29. Content of study • Standard for reporting data is (in principal) decided • in co-operation with the industry • Model-research is on its way (international methods • are 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

30. Illustration Simple model: (intensity) (probability)

31. 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

32. 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

33. 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

34. 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 estimate • these probabilities • These estimates are called t-frequences

35. Estimation termination function • Kaplan-Meier estimator; • product-limit estimator • survival functions • Nelson-Aalen technique; • based on counting process • martingale technique • Statistical properties are well established for • both techniques

36. 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).

37. 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!