2nd Edition

# Actuarial Models The Mathematics of Insurance, Second Edition

656 Pages 107 B/W Illustrations
by Chapman & Hall

654 Pages
by Chapman & Hall

Also available as eBook on:

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.

Preliminary Facts from Probability and Interest
Probability and Random Variables
Expectation
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

A Collective Risk Model for a Short Period
Three Basic Propositions
Counting or Frequency Distributions
The Distribution of the Aggregate Claim

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
Martingales

Global Characteristics of the Surplus Process
A General Framework
Ruin Models
Criteria Connected with Paying Dividends

Survival Distributions
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

Reserves

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

Appendix

References