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MATH20962 Jon Ferns FIA Jon.ferns@btinternet 077 89 487 194 Version: 24 Jan 2014

University of Manchester Contingencies 1 Lecture 1 29 January 2014 “Life tables (lx) and selection by the insurer”. MATH20962 Jon Ferns FIA Jon.ferns@btinternet.com 077 89 487 194 Version: 24 Jan 2014. Course syllabus. Reading materials and information.

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MATH20962 Jon Ferns FIA Jon.ferns@btinternet 077 89 487 194 Version: 24 Jan 2014

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  1. University of ManchesterContingencies 1Lecture 129 January 2014“Life tables (lx) and selection by the insurer” MATH20962 Jon Ferns FIA Jon.ferns@btinternet.com 077 89 487 194 Version: 24 Jan 2014

  2. Course syllabus

  3. Reading materials and information You will need the table book (please pick this up from Stephanie Keegan at the Alan Turing building) - you will need your own copy for all tutorials and to sit the exam: • Institute of Actuaries orange/yellow table book “Formulae and Tables for Examinations of The Institute and Faculty of Actuaries 2002” Standard reading book (optional): • Actuarial Mathematics for Life Contingent Risk (Dickson, Hardy and Waters)Chapters 1-7 covers this course (MATH20962) Calculators allowable in the actuarial exams: • A list can be obtained from the Institute of Actuaries student handbook: http://www.actuaries.org.uk/research-and-resources/documents/student-handbook Material for this course (copies of lectures, tutorials etc) can be found at: • http://www.maths.manchester.ac.uk/undergraduate/ugstudies/units/2013-14/level2/MATH20962/

  4. Exam marks • 20% - Mid course test, more detail to follow next week • 80% - End of course exam • Warning: Although the underlying concepts of this course are relatively straightforward, the exam standard is generally hard and can be time-pressured.

  5. Help Me: 077 89 487 194. Kees Van Schaik: 0161 275 5853 (and in your tutorial)

  6. Notation – 1 year

  7. Notation – n years npx = Probability that a person aged x exact be alive in n years. nqx = Probability that a person aged x exact will die in the next n years npx + nqx = 1 nqx = 1 – npx npx = 1 - nqx

  8. Notation – n years then death

  9. Basic theory Age: I------------------------------I------------------------------------------------------I x x+t x+t+s

  10. Life table construction

  11. Deaths in a life table Probability of death Number of deaths, given lx “alive” at age x

  12. Deferred deaths in a life table

  13. Force of mortality (instantaneous rate of death)

  14. ELT15(males) – example life table

  15. Quiz

  16. Shape of mortality “lx“ (radix l0 approx 50,000)ELT = English Life Table = 3 year survey of England and Wales

  17. Shape of mortality “lx“ (radix l17 =100,000)AM00 = 4 years survey = Assured Males 2000, i.e. “life cover policies” Non smokers smokers

  18. Shape of mortality “dx”

  19. Shape of mortality “qx” 70+. Heavy. (Wide range of diseases.) 40-70 Starting to increase, particularly past age 60. (Heart and cancer) Age 2-40. Light. (A few accidents)

  20. Shape of mortality “qx” (expanded to show the age 0-50 period more clearly) 70+. Heavy. Wide range of diseases. 40-70. Increasing steadily (heart & cancer) Age0-1. Heavy. (some born with medical problems). “Accident hump” Slight increase. (cars-bikes, suicide, drugs). 20-40. Still light. Various causes. Age2-4. Light. (Cot deaths to age 2. Some accidents. Protected environment.)

  21. Other factors affecting mortality (including selection by insurer) Age is not the only factor: • Lifestyle • Sex • Smoking • Wealth (greater wealth implies lower mortality) • Occupation (Office or Manual, Skilled or un-skilled, Dangerous or harmful materials) • Area of the country (Kent / Glasgow) • Where the population has been drawn from must correspond to the purpose for which we intend to use this table: • Experience of the general population (e.g. “ELT15”) • Life assurance policy experience (e.g. “AM92”) • Experience from pension annuities purchased from an insurer (e.g. “PMA92C20”) • Experience from pension annuities for members in an occupational scheme (e.g. “PEN” – in the table book) • Select mortality (period of time after medical underwriting at the start of the policy) => (PTO 3 slides)

  22. “Anti-selection” (by individuals against the insurer) “Anti-selection” by the individuals (not to be confused with “selection” by the insurer) Health Insurance • People will be more likely to want to take out insurance contracts when they believe their risk is higher than the insurance company has allowed for in the premium. This is known as anti-selection. An example in critical illness cover may be where an individual begins to suffer pains in the chest. He takes out a policy without mentioning the chest pains and then goes to the doctor to see if the pains are due to heart disease. If they are, then there is a greater likelihood of a claim for benefit. Anti-selection is also recognised in the tendency for sick or sub-standard lives legitimately to renew policies or take up options providing additional cover without evidence of health. General Insurance • An insurer is exposed to the risk of anti-selection if a policyholder can make use of information not available to the insurer to obtain insurance cover that would not have been granted if the insurer had had the information, or to obtain cover on more favourable terms than would have been granted by the insurer. An insurer may also be exposed to the risk of anti-selection by failing to make use of available, relevant information. Life Insurance • People will be more likely to take out contracts when they believe their risk is higher than the insurance company has allowed for in its premiums. This is known as anti-selection. • Anti-selection can also arise where existing policyholders have the opportunity to exercise a guarantee or an option. Those who have most to gain from the guarantee or option will be the most likely to exercise it.

  23. “Selection” of risks (the insurer weeding out the bad risks and categorising other risks correctly) Examples • Health underwriting on taking out a life cover policy or medical insurance policy => moderately unhealthy lives are charged more=> very high risks are declined altogether • General underwriting on taking out a motor insurance policy MATH20962 concentrates on SELECTION (rather than anti-selection)!!

  24. Select mortality – for life insurance policies The table shows mortality for various people currently aged 50, according to various mortality tables. (Purpose of a select mortality table is to recognise that via its underwriting process at policy inception the insurer has weeded out bad lives from this population of policyholders)

  25. Select mortality notation l[20] = for a person aged 20 now who has just taken out a policy l[19]+1 = for a person aged 20 now who took out a policy when they were aged 19, i.e. they have had the policy 1 year l[18]+2 = for a person aged 20 now who took out a policy when they were aged 18, i.e. they have had the policy 2 years

  26. Select mortality notation AM92 select table for qx from 50 to 54. Aim: calculate the lx. Use a radix of l52 =9660.502 (ultimate)

  27. Select mortality

  28. Select mortality

  29. Select mortality

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