What is an actuary? Presentation Lund University Peter Wohlfart Anna Brinch Nielsen

Transcription

1 What is an actuary? Presentation Lund University Peter Wohlfart Anna Brinch Nielsen

2 What does the graph show?

3 Life expectancy in Sweden

4 Introduction Subject The actuarial profession Work as an actuary Why become an actuary How to become an actuary Purpose Job potentials within mathematical statistics Knowledge about the actuarial profession

5 Introduction Peter Wohlfart - Actuary Educational background Master of Science in Mathematical Statistics (Stockholm University, 2006) Master of Social Science in Economics (Lund University, 2005) Working experience Deloitte Actuarial & Insurance Solutions (Copenhagen, 2005-)

6 Introduction Anna Brinch Nielsen - Actuary Educational background Master of Science in Insurance Mathematics (University of Copenhagen, 2010) Working experience Deloitte Actuarial & Insurance Solutions (Copenhagen, 2007-)

7 Agenda 1. Overall presentation of an actuary 2. Life insurance 3. Non life insurance 4. Modelling of life expectancy 5. Solvency II 6. A&IS, Deloitte 7. Becoming an actuary 8. Questions 9. Useful links 7 Footer

8 Agenda 1. Overall presentation of an actuary 2. Life insurance 3. Non-life insurance 4. Modelling of life expectancy 5. Solvency II 6. A&IS, Deloitte 7. Becoming an actuary 8. Questions 9. Useful links 8 Footer

9 1. Overall presentation of an actuary Actuary = Försäkringsmatematiker Cross-functional profession; combination of Mathematics Probability theory Statistics Computer programming Economy/Finance Law Works at/with insurance companies. Pricing (setting the premiums of insurance contracts) Reserving Risk analysis Reinsurance...

10 1. Overall presentation of an actuary

11 Agenda 1. Overall presentation of an actuary 2. Life insurance 3. Non-life insurance 4. Modelling of life expectancy 5. Solvency II 6. A&IS, Deloitte 7. Becoming an actuary 8. Questions 9. Useful links 11 Footer

12 2. Life insurance Main challenge: Valuation of future cash flows Problem 1: Future cash flows are unknown Problem 2: Present value of future cash flows are unknown Calculation of technical provision ( Reserve ): How much money do we need today to fulfil future obligations? Example 1: 1,000 SEK is paid at time t1 time t0 t1 Discount rate (yearly): r Reserve at time t0:

13 2. Life insurance Example 2: 1,000 SEK is paid at time t1, if the insured is alive at time t1 Scenario 1 time t0 Scenario 2 death t1 No payment time t0 t1 death Payment 1,000 P(insured is alive at t1)=p1 Reserve at time t0:

14 2. Life insurance Example 2: 1,000 SEK is paid at time t1, if the insured is alive at time t1 time t0 t1 What are the risks for the company? Investment return risk Longevity risk

15 2. Life insurance Example 3: 1,000 SEK is paid at time t1, if the insured dies before time t1 Scenario 1 time t0 death t1 Payment 1,000 Scenario 2 time t0 t1 death No payment Reserve at time to:

16 2. Life insurance Example 4: 1,000 SEK is paid at death, if death occurs before time t1 Scenario 1 time t0 Scenario 2 death Payment 1,000 t1 time t0 t1 death No payment Problem: Timing of payment is unknown Technique for calculating reserve: Split the insurance s duration in many small intervall Inside each interval we calculate The payment if the insured event occurs Multiplied by the probability that the insured event occurs Multiplied by the discount factor Sum over all intervals

17 2. Life insurance Example 4: 1,000 SEK is paid at death, if death occurs before time t1 time t0 t1 What are the risks for the company? Investment return risk Mortality risk

18 2. Life insurance Example 5: A benefit is paid each month after the retirement age is reached. The benefits are either: Temporary, e.g. 10 years payments Lifelong Monthly benefits How long is this period? What benefit should be paid? Age Age x Age x+n death

19 Life expectancy in Sweden

20 Agenda 1. Overall presentation of an actuary 2. Life insurance 3. Non-life insurance 4. Modelling of life expectancy 5. Solvency II 6. A&IS, Deloitte 7. Becoming an actuary 8. Questions 9. Useful links 20 Footer

21 3. Non-life insurance Fundamental concept Premium calculation Reserve estimation Premium period

22 3. Non-life insurance Premium

23 3. Non-life insurance Reserve and claim development Incurred But Not Reported Reported But Not Settled Reported But Not Enough Settled

24 3. Non-life insurance Reserve Chain ladder Development year Acc. year Reserve ? ? ? ? ? ?

25 3. Non-life insurance Reserve Chain ladder Development year Acc. year Reserve ? ? ? ? ? ?

26 3. Non-life insurance Reserve Chain ladder Development year Acc. year Reserve ? ? ? ? ? ? Dev. 18% 6% 4% 1% 0%

27 3. Non-life insurance Reserve Chain ladder Development year Acc. year Reserve Dev. 18% 6% 4% 1% 0% 58

28 3. Non-life insurance Reserve Challenges? Data quality and availability Trends Environment Change of legislation Inflation Financial crisis

29 Agenda 1. Overall presentation of an actuary 2. Life insurance 3. Non-life insurance 4. Modelling of life expectancy 5. Solvency II 6. A&IS, Deloitte 7. Becoming an actuary 8. Questions 9. Useful links 29 Footer

30 Life expectancy in Sweden How to hedge the longevity risk?

31 4. Modelling of life expectancy Male and female life expectancy Female Male 65 60

32 Years Modelling of life expectancy Period vs. Cohort life expectancy Cohort and Period Life Expectancy ( ) Cohort Period Time (Year)

33 4. Modelling of life expectancy Introduction Life expectancy not modelled directly Mortality rates are modelled instead Mortality rate = One year probability of dying Split by sex, age and calendar year Life expectancy (period) is calculated based on mortality rates Estimating the mortality rates Based on occurrence and exposure

34 Exposure Modelling of life expectancy Exposure Exposure per age in year 2004 for Danish population Females Rapidly decreasing exposure Small exposure at high ages Uncertainty in estimates Males Age

35 4. Modelling of life expectancy Smoothing Problem: Small exposure for old ages Possible solution: Kernel Smoothing Use additional information from adjacent ages and years AGE 90 AGE CALENDER YEAR CALENDER YEAR

36 Mortality Rate Modelling of life expectancy Smoothing Mortality Rate for Females aged 65 Raw Mortality Estimation Large randomness even if exposure is high Time (Year)

37 Mortality Rate Modelling of life expectancy Smoothing Mortality Rate for Females aged 65 Raw Mortality Estimation Large randomness even if exposure is high Smooth Mortality Estimation Time (Year)

38 4. Modelling of life expectancy The Lee-Carter model ln [m(x,t)] = a(x) + b(x)*k(t) + e(x,t) x=age, t=time a(x): Age-specific constants Describing general pattern of mortality at different ages. k(t): Mortality index Describing the general level of mortality at different times. b(x): Age-specific constants Describing the relative speed of mortality changes when k(t) changes. e(x,t): Error term Constraints: x b( x) 1, k( t) t 0

39 Kappa Modelling of life expectancy The Lee-Carter model ln [m(x,t)] = a(x) + b(x)*k(t) + e(x,t) a(x): Age dependent b(x): Age dependent k(t): Time dependent Only have to forecast k(t) Estimated ( ) and Predicted ( ) Kappa Estimated Kappa Estimation Period ( ) Time (Year)

40 Kappa Modelling of life expectancy The Lee-Carter model ln [m(x,t)] = a(x) + b(x)*k(t) + e(x,t) a(x): Age dependent b(x): Age dependent k(t): Time dependent Only have to forecast k(t) Estimated ( ) and Predicted ( ) Kappa Estimated Kappa Estimated Kappa Estimation Period ( ) Estimation Period ( ) Prediction Period Prediction Period ( ) Time (Year)

41 Years Modelling of life expectancy Length of estimation period Remaining Life Expectancy for Male aged 65 Short estimation period ( ) Long estimation period ( ) Prediction period ( ) Time(Year) 41

42 Years Modelling of life expectancy Length of estimation period Remaining Life Expectancy for Male aged 65 Short estimation period ( ) Short estimation Period 18,4 years Long estimation period ( ) Prediction period ( ) Time(Year) 42

43 Years Modelling of life expectancy Length of estimation period Remaining Life Expectancy for Male aged 65 Short estimation period ( ) Short estimation Period 18,4 years Long estimation period ( ) Long estimation Period 16,4 years Prediction period ( ) Time(Year) 43

44 4. Modelling of life expectancy Other challenges Population mortality differ from insurance mortality Insured individuals tend to live longer Limitations in insurance administration systems Standard mortality model is used Gompertz Makeham mortality: Simple and well known Used by the most insurance companies Does not capture future improvements in mortality How to capture future improvements? Multiply with a calendar year factor (e.g. 0,98^t) Use different parameters for different generations Don t capture

45 Agenda 1. Overall presentation of an actuary 2. Life insurance 3. Non-life insurance 4. Modelling of life expectancy 5. Solvency II 6. A&IS, Deloitte 7. Becoming an actuary 8. Questions 9. Useful links 45 Footer

46 5. Solvency II Risk based assessment New legislation Pillar 1: Quantitative requirement Pillar 2: Governance Pillar 3: Disclosure & Transparancy Complementary to standard balance sheet Solvency capital requirement

47 5. Solvency II Quantitative Impact Studies 5 (QIS 5) SCR Adj BSCR SCR Op Correlation SCR NonLife SCR Market SCR Default SCR Health SCR Life SCR Intang Correlation Correlation Correlation Correlation Premium and reserve Equity Health SLT Lapse Mortality Lapse Spread Interest rate Concentration Health Non- SLT Longevity Life Cat CAT Property Currency Health CAT Disability Morbidity Revision Illiquidity Life Expense

48 5. Solvency II Catastrophe risk SW Code Country Population Arena Location Capacity Sweden Nya Ullevi Gothenburgh ) Input the country information in the light blue cells (risk results are computed in the dark blue cells) Arena Concentration Pandemic Country risk Arena Concentratio n Pandemic Arena Concentration Pandemic Injury proportion Policyholders Average sum insured Total sum insured Injury risk Type of injury PH p Ep Ep Ep Accidental death 10,0% Permanent total disability 1,5% Long term disability 5,0% Short term disability 13,5% Medical/Injuries 30,0% Largest known concentration of lives insured, for concentration risk 22

49 Agenda 1. Overall presentation of an actuary 2. Life insurance 3. Non-life insurance 4. Modelling of life expectancy 5. Solvency II 6. A&IS, Deloitte 7. Becoming an actuary 8. Questions 9. Useful links 49 Footer

50 6. A&IS, Deloitte Actuarial & Insurance Solutions The largest actuarial practice in Denmark The leading practice in the Scandinavian market 15 actuaries in Copenhagen Danish, Norwegian, Swedish, Romanian and American background Local knowledge in a global network Specialized knowledge in a local network Striving to be the leading actuarial practice in the world A service line in the financial sector 50

51 6. A&IS, Deloitte Actuarial topics Audit Solvency II (+QIS 5) IFRS Product development General advisory A&IS products Captives Reserve review Embedded Value M&A Risk management / ALM Consultancy vs. Insurance company

52 Agenda 1. Overall presentation of an actuary 2. Life insurance 3. Non-life insurance 4. Modelling of life expectancy 5. Solvency II 6. A&IS, Deloitte 7. Becoming an actuary 8. Questions 9. Useful links 52 Footer

53 7. Becoming an actuary Why become an actuary?

54 7. Becoming an actuary How to become an actuary? Aktuarieprogrammet - Masterprogram i försäkringsmatematik Stockholm University Matematiska institutionen: 2 years masters programme Basic education: Bachelor degree in mathematics or mathematical statistics Gives the educational requirements to work as an responsible actuary in Sweden, according to the requirements from Finansinspektionen The programme includes courses in: Insurance mathematics Financial mathematics Insurance law Insurance economy University of Copenhagen

55 Agenda 1. Overall presentation of an actuary 2. Life insurance 3. Non-life insurance 4. Modelling of life expectancy 5. Solvency II 6. A&IS, Deloitte 7. Becoming an actuary 8. Questions 9. Useful links 55 Footer

56 8. Questions Contact details Actuary Peter Wohlfart Manager Actuary Anna Brinch Nielsen Consultant

57 Agenda 1. Overall presentation of an actuary 2. Life insurance 3. Non-life insurance 4. Modelling of life expectancy 5. Solvency II 6. A&IS, Deloitte 7. Becoming an actuary 8. Questions 9. Useful links 57 Footer

58 9. Useful links Masterprogram i försäkringsmatematik Actuary at University of Copenhagen (Danish/English) Svenska Aktuarieföreningen Den Danske Aktuarforening Bliv aktuar A&IS, Deloitte ndex.htm

59 Deloitte Touche Tohmatsu Limited Deloitte refers to one or more of Deloitte Touche Tohmatsu Limited, a UK private company limited by guarantee, and its network of member firms, each of which is a legally separate and independent entity. Please see for a detailed description of the legal structure of Deloitte Touche Tohmatsu Limited and its member firms. Statsautoriseret Revisionsaktieselskab. Member of Deloitte Touche Tohmatsu Limited