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  • Week 1: Revision of Actuarial Mathematics I

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  • Module Description

    Welcome to Actuarial Mathematics II. In this section you will find important information about how the module will run, the syllabus and assessments.

    Lectures and Seminars

    There will be 4 timetabled hours per week for this module on Thursdays and Fridays  . In general there will be 2-3 hours of lectures with new material and 2-1 hours of 'seminar' where we will go over example questions.

    Office hour: Thursday 12:00-1:00PM in the Student Hub

    Getting Help

    If you have any questions about the module or the content please do arrange an online 'office-hour' meeting with Melania (m.nica@qmul.ac.uk) or use the Student Forum section of the module QM Plus page to ask questions as we go.

    Assessment

    Assessment for this module is 70% final exam in the May / June assessment  plus two assessed courseworks each accounting for 15% of the module mark. The assessed courseworks will both involve calculations using MS Excel based on the material taught in this module. These will be set in week 6 and week 9 with more details under those two sections of the QM Plus site.


    Useful Tables and Formulae

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  • Syllabus


    • The syllabus for MTH5125 covers approximately 60% of the Institute & Faculty of Actuaries CM1 exam syllabus.

      ·       Describe the principles of actuarial modelling

      ·       Define various assurance and annuity contracts

      ·       Develop formulae for the means and variances of the payments under various assurance and annuity contracts, assuming constant deterministic interest rate

      ·       Define and use assurance and annuity functions involving two lives

      ·       Describe and illustrate methods of valuing cashflows that are contingent upon multiple transition events

      ·       Describe and use methods of projecting and valuing expected cashflows that are contingent upon multiple decrement events

      ·       Define the gross random future loss under an insurance contract, and state the principle of equivalence

      ·       Describe and calculate gross premiums and reserve of assurance and annuity contracts

      ·       Define and calculate for a single policy or a portfolio of policies (as appropriate) death strain at risk, expected death strain, actual death strain and mortality profit for policies with death benefits payable immediately on death or at the end of the year of death, policies paying annuity benefits at the start of the year or on survival to the end of the year and policies where single or non-single premiums are payable

      ·       Project expected future cashflows for whole life, endowment and term assurances, annuities, unit-linked contracts and conventional/unitised with profits contracts, incorporating multiple decrement models as appropriate

      ·       Show how, for unit-linked contracts, non-unit reserves can be established to eliminate future negative cashflows, using a profit test model

    • AM92 Mortality Table File
      1019.1 KB

  • Learning outcomes

    The learning outcomes for this module are:

    Academic Content

    • life contingent actuarial mathematics
    • premiums, reserves and profits for a variety of life assurance contracts both traditional and unit-linked, including those dependent on two lives
    • contingencies dependent on multiple transitions or multiple decrements

    Disciplinary Skills

    • application of probability and actuarial mathematics to financial calculations in life assurance and pensions
    • analysis of the financial and actuarial implications of these calculations
    • using MS Excel to perform calculations
    • report writing

    Graduate Attributes

    • use information for evidence-based decision making
    • apply analytical skills to investigate unfamiliar problems
    • connect information and ideas within the field of study

  • Assessment

      • Two in-term assessments (analytical, using Excel) accounting for 30% of the final mark
      • Final Exam accounting for 70% of the final mark

    • AM92 Mortality Table File
      1019.1 KB
    • Exam Formula Sheet File
      1.3 MB

  • Past exam papers

    Assessment for this module is 70% final exam in the May / June assessment  plus two assessed courseworks each accounting for 15% of the module mark. The assessed courseworks will both involve calculations using MS Excel based on the material taught in this module. These will be set in week 6 and week 9 with more details under those two sections of the QM Plus site.

    For the final exam, there will be past papers from previous years available on QM Plus in the week 12 section.

    For actuarial students, your score in this module along with that in Actuarial Mathematics I will count towards possible exemption from the Institute and Faculty of Actuaries CM1 examination. 

    More information on IFoA exemptions for actuarial students is available at https://qmplus.qmul.ac.uk/mod/page/view.php?id=597978 ;

  • Q-Review

  • Week 2 - Premiums

    This week we will look at key calculations in life assurance - premiums (net and gross). These are fundamental to the operation of a life assurance company and the ways in which these companies are regulated around the world. 



  • Week 3 - Reserves

    This week we start looking at why life assurance companies hold reserves. We  also look at methods of determining policy values . We  also continue with Practice Set 1 (from last week) and we introduce new exercises on Reserves if time permits. 

  • Week 4 -Retrospective Policy Values


    We start first with Retrospective Policy values. 

    On Thursday we do Exercise 6.3 from Practice Set 1 with Excel and start working on Practice Set 2. On Friday we continue with Excel Exercises.

  • Week 5 - Mortality Profit and Two Lives

    This week we start a new topic - Mortality Profit. 

    Then we move on to life assurance policies involving two lives (for two weeks). We will consider premiums and reserves for a variety of different policies. Given that mortgages are very often taken out by two people and that many pension funds include payments to a surviving partner, these "two lives" insurance functions are often used in practice. 


  • Week 6 - Joint Life Part 2

    This week we will complete the topic on Life Assurance for Two Lives.
    After the reading week, in weeks 8 and 9 we will look at techniques that can be applied to health insurance as well as life assurance.

    The first assessed coursework will be released this week on Friday (March 1st).

  • 1st assessed coursework due Friday 15th March

    This first assessed coursework is based on material from the first 6 weeks of the module. The submission deadline is 5:00pm UK time on Friday, March 15. 

  • Week 7 - Lecture only on Friday - revision of what we have done so far

  • Week 8 - Multiple States

    This week we consider actuarial techniques used in Health Insurance and other areas where there are "competing risks" and insurance benefits that are payable on different events. Over weeks 8 and 9 we explore two methods for dealing with these: Multi State Models and Multi Decrement Tables. 

  • Week 9 - Multiple States: Reserves

    This week we continue with Multiple States and introduce Reserves 

  • Week 10 -Multiple decrements models

    Multiple Decrement models and tables. These are used by actuaries in health insurance and in pensions. 

  • 2nd assessed coursework - due Thursday, April 11

    The submission deadline is 5:00pm UK time on Thursday April 11 (week 12). Below you will find a file with the task and submission instructions and the submission point to upload 2 files by the deadline. 

  • Week 11 - Pension Models

    We will look at Pension models - as applications of multiple state, and multiple decrements models. We will complete the lecture material for this module with cash flow analysis and equity linked life assurance policies.

  • Week 12: Revision

    This week will complete the revision and do exercises from past exams.