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Useful for ISS

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  1. Welcome
  2. Course Outcomes
  3. Units in this Course
  4. 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

  1. Define insurance and identify its various applications.
  2. Understand and apply principles of premium calculation.
  3. Work with survival models and construct/use life tables.
  4. Develop the foundations needed for the life-insurance industry.
  5. 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.
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.
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Next course in learning order: Advanced Actuarial Statistics Applied statistics