Actuarial Models: The Mathematics of Insurance, Second Edition, 2nd Edition (e-Book) book cover

Actuarial Models

The Mathematics of Insurance, Second Edition, 2nd Edition

By Vladimir I. Rotar

Chapman and Hall/CRC

654 pages | 107 B/W Illus.

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pub: 2014-08-18
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Actuarial Models: The Mathematics of Insurance, Second Edition thoroughly covers the basic models of insurance processes. It also presents the mathematical frameworks and methods used in actuarial modeling. This second edition provides an even smoother, more robust account of the main ideas and models, preparing students to take exams of the Society of Actuaries (SOA) and the Casualty Actuarial Society (CAS).

New to the Second Edition

  • Revises all chapters, especially material on the surplus process
  • Takes into account new results and current trends in teaching actuarial modeling
  • Presents a new chapter on pension models
  • Includes new problems from the 2011-2013 CAS examinations

Like its best-selling, widely adopted predecessor, this edition is designed for students, actuaries, mathematicians, and researchers interested in insurance processes and economic and social models. The author offers three clearly marked options for using the text. The first option includes the basic material for a one-semester undergraduate course, the second provides a more complete treatment ideal for a two-semester course or self-study, and the third covers more challenging topics suitable for graduate-level readers.

Table of Contents

Preliminary Facts from Probability and Interest

Probability and Random Variables


Some Basic Distributions

Moment Generating Functions

Convergence of Random Variables and Distributions

Limit Theorems

Conditional Expectations. Conditioning

Elements of the Theory of Interest

Comparison of Random Variables. Preferences of Individuals

A General Framework and First Criteria

Comparison of R.V.s and Limit Theorems

Expected Utility

Non-Linear Criteria

Optimal Payment from the Standpoint of an Insured

An Individual Risk Model for a Short Period

The Distribution of an Individual Payment

The Aggregate Payment

Premiums and Solvency. Approximations for Aggregate Claim Distributions

Some General Premium Principles

A Collective Risk Model for a Short Period

Three Basic Propositions

Counting or Frequency Distributions

The Distribution of the Aggregate Claim

Premiums and Solvency. Normal Approximation

Random Processes and Their Applications I

A General Framework and Typical Situations

Poisson and Other Counting Processes

Compound Processes

Markov Chains. Cash Flows in the Markov Environment

Random Processes and Their Applications II

Brownian Motion and Its Generalizations


Global Characteristics of the Surplus Process

A General Framework

Ruin Models

Criteria Connected with Paying Dividends

Survival Distributions

The Probability Distribution of Lifetime

A Multiple Decrement Model

Multiple Life Models

Life Insurance Models

A General Model

Some Particular Types of Contracts

Varying Benefits

Multiple Decrement and Multiple Life Models

On the Actuarial Notation

Annuity Models

Two Approaches to the Evaluation of Annuities

Level Annuities. A Connection with Insurance

Some Particular Types of Level Annuities

More on Varying Payments

Annuities with m-thly Payments

Multiple Decrement and Multiple Life Models

Premiums and Reserves

Premium Annuities


Pensions Plans

Valuation of Individual Pension Plans

Pension Funding. Cost Methods

Risk Exchange: Reinsurance and Coinsurance

Reinsurance from the Standpoint of a Cedent

Risk Exchange and Reciprocity of Companies

Reinsurance Market



Answers to Exercises


Exercises appear at the end of each chapter.

Subject Categories

BISAC Subject Codes/Headings:
MATHEMATICS / Probability & Statistics / General