2nd Edition

Actuarial Models The Mathematics of Insurance, Second Edition

By Vladimir I. Rotar Copyright 2015
    656 Pages 107 B/W Illustrations
    by Chapman & Hall

    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
    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.


    Vladimir I. Rotar