This course aims:
- to introduce some more advanced topics in life insurance mathematics, and complete the material covered in Subject CT5
- Thiele’s differential equation
- Markov multiple-state models
- risk reserves
- insurances written on multiple lives
- the features of disability and long-term care insurance and pension contracts
- heterogeneity and selection
- single-figure indices
- profit testing conventional insurance contracts
- profit testing unit-linked contracts
Course Description: Link to Official Course Descriptor.
Pre-requisite course(s): F70LA Life Insurance Mathematics A .
Learning Outcomes: Subject Mastery
At the end of studying this course the students should be able to do or understand the following:
- derive Thiele’s differential equation for standard insurance benefits, and solve it numerically using an Euler scheme
- define Markov life-history models in terms of states, transitions and transition intensities
- state and prove Kolmogorov’s forward equations, state Thiele’s differential equations, and use an Euler scheme to solve both numerically, for a general Markov multiple-state model
- calculate risk reserves for simple homogeneous life insurance portfolios
- define models for the joint life histories of two individuals; (a) as a multiple-state model; and (b) in terms of random future lifetimes
- calculate expected present values, premiums and policy values for the following types of joint-life policies: first-death and second-death assurances and annuities, reversionary annuities, and contingent assurances
- describe the main features of disability insurance, long-term care insurance and defined-benefit pension schemes
- understand possible sources of heterogeneity, its effect on the analysis of insurance data, and its possible impact on insurance business
- construct single figure indices to summarise mortality and other experiences, and understand the strengths and weakness of each
- calculate the profit vector, profit signature, net present value, profit margin, discounted payback period, and internal rate of return for conventional policies
- describe the effect on the profit vector of changes in the premium, valuation, and experience bases
- describe the operation of the unit price and the charging structure for unit-linked policies
- calculate the unit fund, sterling fund, sterling reserve, and measures of profit for unit-linked policies
- Formulae and Tables for Actuarial Examinations
- Introduction to Survival Models, Volumes 2 and 3 Hardy, Macdonald, Waters and McCutcheon.
F70LB is assessed by a two-hour exam in April/May (80%) and an Excel-based assignment (20%). The course is synoptic with F70LA (Life Insurance Mathematics A).
SCQF Level: 10.
Help: If you have any problems or questions regarding the course, you are encouraged to contact the lecturer
VISION: further information and course materials are available on VISION