2nd Edition
Actuarial Models The Mathematics of Insurance, Second Edition
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
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
Martingales
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
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
Answers to Exercises
Index
Exercises appear at the end of each chapter.
Biography
Vladimir I. Rotar
