Contingencies 2

MATH39522 Contingencies 2 10 Semester 2 Undergraduate Level 3 Jonathan Ferns Unit coordinator Department of Mathematics 1 FHEQ level (Framework for Higher Education Qualifications) ' Last part of a Bachelors ' European Credit Transfer & Accumulation System Rating : 5.0 This unit is a continuation of MATH20962 (Contingencies 1) and covers the remaining part of the material required in subject CM1 of the Actuarial Profession's examinations.In Contingencies 1 we looked at one life who may be in one of two states, alive or dead.In Contingencies 2 we will consider assurances and annuities where payments are contingent on the lives of two people (e.g. an assurance that pays out when the second of two people dies or an annuity that only pays if two people are both alive). We will also consider models with more than two states (e.g. (i) alive and healthy or (ii) alive but ill or (iii) dead).We will also look again at the recursive formula which links reserves but, in Contingencies 2, will use this to analyse profits. We will finally study mortality a bit more.   This unit is a continuation of MATH20962 (Contingencies 1) and covers the remaining part of the material required in subject CM1 of the Actuarial Profession's examinations. In Contingencies 1 we looked at one life who may be in one of two states, alive or dead. In Contingencies 2 we will consider assurances and annuities where payments are contingent on the lives of two people rather than one and also consider models with more than two states (e.g. (i) alive and healthy or (ii) alive but ill or (iii) dead).We will also examine the cash flows and profit measures for each year of a policy, including for a wider range of insurance policies than studied in MATH20962.   The course aims to provide further mathematical instruction in models using cashflows which depend upon survival, death and other uncertain factors. These have practical application in more complex forms of life assurance, health insurance and pension provision than was seen in MATH20962.  On completion of this course unit students will be able to: <ol> <li aria-setsize="-1" data-aria-level="1" data-aria-posinset="1" data-font="" data-leveltext="%1." data-listid="1" role="listitem">Develop formula and associated probabilities¿for and calculate expected present values (using either the standard R functions used in the course, by hand or using simple integration techniques) for assurances and annuities for joint life policies, last survivor policies and also policies where the order in which death might occur is a factor. Use these to calculate premiums and reserves for policies. </li> <li aria-setsize="-1" data-aria-level="1" data-aria-posinset="2" data-font="" data-leveltext="%1." data-listid="2" role="listitem">Write down integrals for the expected present value of benefits subject to competing risks (e.g. retirement and death) defined by a Markov model. </li> <li aria-setsize="-1" data-aria-level="1" data-aria-posinset="3" data-font="" data-leveltext="%1." data-listid="3" role="listitem">Recognise the difference between the forces of transition, dependent rates of transition and independent rates of transition and be able to calculate one from another. </li> <li aria-setsize="-1" data-aria-level="1" data-aria-posinset="4" data-font="" data-leveltext="%1." data-listid="4" role="listitem">Use the forces and rates of transition described in 3. correctly in the context of both Multi State Modelling and the development and application of a Multiple Decrement Tables to calculate expected present values. </li> <li aria-setsize="-1" data-aria-level="1" data-aria-posinset="5" data-font="" data-leveltext="%1." data-listid="5" role="listitem">Develop formula to calculate the expected present value of defined benefit pension schemes and use the standard functions developed in R to calculate their value. Apply these to various settings found in practice. </li> <li aria-setsize="-1" data-aria-level="1" data-aria-posinset="6" data-font="" data-leveltext="%1." data-listid="6" role="listitem">Develop formula for and calculate the profit vector, profit margin and Internal Rate of Return for both conventional and Unit Linked policies. </li> <li aria-setsize="-1" data-aria-level="1" data-aria-posinset="7" data-font="" data-leveltext="%1." data-listid="7" role="listitem">Describe why insurers zeroise their reserves and demonstrate how to do this. </li></ol>  TIn more detail, the unit explores the following financial topics from a mathematical point of view.1. Annuities and Assurances involving two lives. These include assurances that pay out on the first death/annuities that cease payment on the first death, and also assurances that pay out/annuities that stop on the second death. Also studied are policies where the order in which death occurs is key - for example, for two lives x and y, a policy that pays out if x dies first but not if life y dies. The calculation of the expected present values (EPV) of these policies, together with the probabilities that underpin these EPVs. The use of these EPVs to calculate premiums and reserves.2. Policies where there are more than 2 states, How, for example, the probability of death is influenced by the probability of becoming ill, and vice versa, or, for somebody already ill, how the probability of death is influenced by the probability of recovery. Formula are developed for the calculation of the associated probabilities and the evaluation of EPVs.  3. A subset of the above which considers a simplified model (called a Multiple Decrement Model) from which probabilities and EPV calculations can be readily made.4. Using the Multiple Decrement Model to extend the idea of the life table from Contingencies 1 (a single decrement table) to a table allowing for additional decrements to death, such as retirement or sickness (a multiple decrement table).5. Pension Schemes in the UK covering the different types of pension scheme and the use of a given Multiple Decrement Table to calculate the EPV of pension benefits and premium payments (called contributions). Some practical problems in pensions are also studied.6. The calculation of expected cash flows for conventional policies (studied in Contingencies 1) and also a new type of policy known as a unit linked policy. The principles for measuring profit for each individual year for a policy is studied together with an alternative way to calculate reserves (referred to as zeroisation). Overall profit measures for the lifetime of a policy are also explored, alongside the profitability criteria for deciding to introduce a new policy.  0 Other 20% 1 Written exam 80% One short, in-class test worth 20% and an optional non-credit bearing mock test also held in class.End of semester examination: weighting 80% Feedback tutorials will provide an opportunity for students' work to be discussed and provide feedback on their understanding.  Coursework or in-class tests (where applicable) also provide an opportunity for students to receive feedback.  Students can also get feedback on their understanding directly from the lecturer, for example during the lecturer's office hour. MATH20962 Contingencies 1 - Actuarial Science Pre-Requisite Compulsory MATH39522 Requisites: (A) MATH20962; (B) Unit can be taken by Actuarial Science students only.Available to Actuarial Science and Maths students only N Essential: Long form Course notes are provided. These are available on Black Board and cover all the material needed for the course.Recommended: If you wish to read around the course and access some further examples then go to:D.C.M. Dickson, M.R. Hardy and H.R. Waters, Actuarial Mathematics for Life Contingencies. Lectures 24 Tutorials 17 0 59