Actuarial Statistics
Useful for ISS
On this page
- Welcome
- Course Outcomes
- Units in this Course
- Recommended Textbooks
Welcome
This is the complete study package for Actuarial Statistics — the mathematical
foundation of insurance and pension industries. The course covers utility theory, premium
principles, survival distributions, life-insurance models and life-annuities. Every concept
comes with two worked examples.
Pre-requisite: The earlier subjects — especially distributions, expectation and
the MGF — and Inferential Statistics. Some familiarity with the life tables and
fertility/mortality rates met in Applied Statistics is helpful.
Course Outcomes
- Define insurance and identify its various applications.
- Understand and apply principles of premium calculation.
- Work with survival models and construct/use life tables.
- Develop the foundations needed for the life-insurance industry.
- Effectively understand insurance annuities and premium plans.
Units in this Course
UNIT 1
Introductory Statistics, Insurance & Utility
Discrete, continuous & mixed distributions; insurance applications; sum of random variables; utility theory — utility functions, expected utility criterion, types of utility function, insurance and utility.
UNIT 2
Premium Principles & Individual Risk Models
Properties & examples of premium principles; individual risk models — models for individual claims, sum of independent claims, approximations and applications.
UNIT 3
Survival Distribution & Life Tables
Age at death, survival function, time-until-death, curtate future lifetime, force of mortality; life tables & deterministic survivorship group; assumptions for fractional ages; analytical laws of mortality.
UNIT 4
Life Insurance
Models for insurance payable at the moment of death & at the end of the year of death; actuarial present values, net single premiums and the relationships between continuous and discrete forms.
UNIT 5
Life Annuities & Premiums
Continuous & discrete life annuities, annuities with periodic payments; computation of continuous and discrete premiums; equivalence principle.
PRACTICAL
Practical Course (8 Experiments)
Risk under utility models; aggregate-claim calculations; ruin probabilities; annuities & present values; premium computation; life-model practicals.
REFERENCE
Official Syllabus
Course outline, textbooks, references and exam blueprint.
Recommended Textbooks
- C. M. D. Dickson (2005) — Insurance Risk and Ruin.
- Bowers, Gerber, Hickman, Jones & Nesbitt (1997) — Actuarial Mathematics, Society of Actuaries.
- S. R. Deshmukh (2009) — Actuarial Statistics: An Introduction Using R.
- Harriett E. J. & Dani L. L. (1999) — Principles of Insurance: Life, Health, and Annuities, LOMA.
Standard actuarial notation uses subscripts heavily — e.g. \(l_x, q_x, p_x, A_x, \bar a_x\). All of these are introduced gradually through the units; a quick-reference table is on the Syllabus page.
Next course in learning order: Advanced Actuarial Statistics Applied statistics