Module Details |
The information contained in this module specification was correct at the time of publication but may be subject to change, either during the session because of unforeseen circumstances, or following review of the module at the end of the session. Queries about the module should be directed to the member of staff with responsibility for the module. |
Title | Life Insurance Mathematics II | ||
Code | MATH373 | ||
Coordinator |
Dr M Boado Penas Mathematical Sciences Carmen.Boado@liverpool.ac.uk |
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Year | CATS Level | Semester | CATS Value |
Session 2016-17 | Level 6 FHEQ | First Semester | 15 |
Aims |
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Learning Outcomes |
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Be able to explain, define and analyze the joint survival functions. |
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Understand the concept (and the mathematical assumptions) of the joint future life time random variables in continuous and discrete time and monthly. Be able to derive the distributions and the moment/variance of the joint future lifetimes. |
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Be able to define the survivals probabilities/death probabilities of either or both two lives, explain these types of probabilities and the force of interest intuitively, be able to calculate the different types of the survival/death probabilities in theoretical and numerical examples. | |
Understand, define and derive the expected present values of different types of the life assurances and life annuities for joint lives, be able to calculate the expected present values of the joint life assurances and life annuities in theoretical and numerical examples. |
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Be familiar with R solfware and uses in actuarial mathematics |
Syllabus |
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1 |
(a) Revision of Life insurance I (c) Multiple life models (Markov / semi-Markov models) The death-alive model, term insurance with increasing benefit on accident death, the permanent disability model, the disability income insurance model, the joint life and last survivor model, assumptions of the models, probabilities based on intensities using Kolmogorov’s equations, transition intensities based on probabilities, numerical evaluation of probabilities. (d) Emergency costs for all contract types and pensions Unit-linked contracts and disability long-term contracts, profit test annual premium contracts, the profit vector, the net present value, the profit signature, the profit margin, the profit test to price a product/determine reserves, construction and use of a multiple decrement service table for pension calculation, extension of the above techniques to calculate expected cash flows contingent risk other than human lives.
(e) Selection and heterogeneity
Principal factors which contribute to the variation in mortality and morbidity by region and according to: occupation, nutrition, housing, geography, education. Examples of main forms of selection: temporary or initial selection, class selection, time selection, spurious selection, adverse selection, necessity of different mortality tables for different classes of lives, the theoretical basis of the use of risk classification in life insurance, definitions of the terms: crude index, direct/indirect standardization, standardized mortality/ morbidity rate, SMR.
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Recommended Texts |
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Reading lists are managed at readinglists.liverpool.ac.uk. Click here to access the reading lists for this module. Explanation of Reading List: Key textbook D.C.M., Dickson, M.R., Hardy, H.R., Waters, (2009), Actuarial Mathematics for Life Contingent Risks, Cambridge University Press.Recommended textbook [1] H.U., Gerber, (1997), Life Insurance Mathematics, Spinger. [2] H.U., Gerber, J., Hickman, D., Jones, C., Nesbitt, N., Bowers, (1997), Actuarial Mathematics, 2nd Edition, Society of Actuaries . [3] Formulae and Tables, (2002), The Faculty of Actuaries & The Institute of Actuaries. [4] S. Haberman, E., Pitacco, (1999), Actuarial models for Disability Insurance, Chapman & Hall/CRC. [5] A.E., Easton, T.M., Harris, (1999), Actuarial Aspects of Individual Life Insurance and Annuity Contracts, ACTEX Publications. |
Pre-requisites before taking this module (other modules and/or general educational/academic requirements): |
MATH273; MATH162; MATH101; MATH102 |
Co-requisite modules: |
Modules for which this module is a pre-requisite: |
Programme(s) (including Year of Study) to which this module is available on a required basis: |
Programme:NG31 Year:3 |
Programme(s) (including Year of Study) to which this module is available on an optional basis: |
Assessment |
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EXAM | Duration | Timing (Semester) |
% of final mark |
Resit/resubmission opportunity |
Penalty for late submission |
Notes |
Unseen Written Exam | 2.5 hours | First Semester | 100 | Yes | Standard UoL penalty applies | Assessment 1 Notes (applying to all assessments) Written Exam - All 5 questions carry equal weight. |
CONTINUOUS | Duration | Timing (Semester) |
% of final mark |
Resit/resubmission opportunity |
Penalty for late submission |
Notes |