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goldenbin
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楼主

发表于 2003-11-9 12:15:08 |只看该作者 |倒序浏览

By Kenwind

Course 1 – Mathematical Foundations of Actuarial Science

This course is jointly administered by the SOA and CAS.

The examination for this course consists of four hours of multiple-choice questions and is identical to CAS Exam 1.
The purpose of this course is to develop a knowledge of the fundamental mathematical tools for quantitatively assessing risk. The application of these tools to problems encountered in actuarial science is emphasized. A thorough command of calculus and probability topics is assumed. Additionally, a very basic knowledge of insurance and risk management is assumed.

The tools emphasized are:

Limits, series, sequences and functions;

Derivatives of single and multivariate functions (maximums, minimums, constrained maximums and minimums, rate of change);

Integrals of single and multivariate functions, simple differential equations;

Parameterized curves;

General probability (set functions, basic axioms, independence);

Bayes' Theorem;

Univariate probability distributions (probabilities, moments, variance, mode, percentiles, transformations);

Multivariate probability distributions (Central Limit Theorem; joint, conditional and marginal distributions-probabilities, moments, variance, covariance).
A table of values for the normal distribution will be included with the examination booklet.

Suggested Texts
The texts listed below are considered representative of the many texts used by colleges and universities in Canada and the US to cover material on which the candidate may be examined. Earlier or later editions of the listed texts contain essentially the same material and should be adequate for review purposes. In addition there are study notes for this course. The candidate is expected to be familiar with the concepts introduced in the study notes.

Calculus

Calculus (Seventh Edition), 2002, by Larson, R.E., Hostetler, R.P. and Edwards, B.H.

Calculus: Concepts and Contexts (Second Edition), 2001, by Stewart, J.

Calculus: Graphic, Numerical and Algebraic, 1999, by Finney, R.L., Demana, F.D. and Waits, B.K.

Calculus: Late Transcendentals (Seventh Edition), 2001, by Anton, H., Bivens, I. and Davis, S.

Calculus with Analytic Geometry (Fifth Edition), 1997, by Edwards, C.H. and Penney, D.E.
Probability

A First Course in Probability (Sixth Edition), 2001, by Ross, S.M., Chapters 1-8.

Fundamentals of Probability (Second Edition), 1999, by Ghahramani, S., Chapters 1-10.

Probability for Risk Management, 1999, by Hassett, M. and Stewart, D., Chapters 1-11.

Probability and Statistical Inference (Sixth Edition), 2001, by Hogg, R.V. and Tanis, E.A.,
Chapters 1-6.

Probability: The Science of Uncertainty with Applications to Investments, Insurance and Engineering 2001, by Bean, M.A., Chapters 1-9.

Study Notes
SNs for Courses 1-6 are available on our Web site in the Education and Examination area under "Study Notes/Information." Hard copies may be purchased by using the Study Note and Published Reference order form in the back of the printed catalog or on the "Study Notes/Information" Web page.

Code Title
1-05-03# Course 1 Inroductory Study Note
Tables for the Course 1 Examination
1-12-00 November 2000 Course/Exam 1
1-10-01 May 2001 Course/Exam 1
1-12-01 November 2001 Course/Exam 1
1-21-00 Risk and Insurance

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goldenbin
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沙发

发表于 2003-11-9 12:16:16 |只看该作者

Course 2 – Interest Theory, Economics and Finance

This course is jointly administered by the SOA and CAS.

The examination for this course consists of four hours of multiple-choice questions and is identical to CAS
Exam 2.

This course covers interest theory (discrete and continuous), intermediate microeconomics and macroeconomics and the fundamentals of finance. It assumes a basic knowledge of calculus and probability.
A table of values for the normal distribution will be included with the examination booklet.

Learning Objectives
A. Economics

Microeconomics
Candidates should be able to use the following microeconomic principles to build models to increase their understanding of the framework of contingent events and to use as a frame for activities such as pricing:
The shape of the Demand Curve, demand versus quantity demanded, changes in demand, and market demand,

The supply versus quantity supplied equilibrium and the point of equilibrium and changes in the equilibrium point,

Tastes, indifference curves and the Marginal Rate of Substitution,

Changes in income and the budget line, the Engel Curve,

Changes in price and changes in the budget line, the Demand Curve,

Income and substitution effects, the Compensated Demand Curve, why Demand Curves slope downward,

Decisions under uncertainty such as the following: attitudes toward risk and the risk and theory of rational expectations,

Adverse selection and moral hazard.

Candidates should be able to use knowledge of the following microeconomic principles to increase their understanding of the markets in which we operate and of the regulatory issues, also to use the following microeconomic principles to increase their understanding of the ramification of strategic decisions:
The competitive firm, the competitive industry in the short run, revenue, costs and supply, elasticity of supply, competitive equilibrium,

The competitive firm, the competitive industry in the long run, long run costs, supply profits, constant/decreasing-cost industries, and equilibrium,

Sources of monopoly power: natural, patents, resources, and legal barriers,

Oligopoly, contestable markets, a fixed number of firms,

Collusion, game theory, the prisoner's dilemma, and the breakdown of cartels,

Monopolistic competition, product differentiation and the economics of location,

Consumers' and producers' surplus economics, theories of values,

Adverse selection and moral hazard.
Macroeconomics
Candidates should understand the following macroeconomic principles and use them in developing economic models and/or economic assumptions:
The general accounting conventions and data sources used in tracking economic activity,

The simplified Keynesian model, without adjustments for changes in price level or money supply, as it applies to changes in GDP caused by changes in investment, government spending, and net exports, mong interest rates, demand for money, consumption and investment using concepts such as the IS/LM curve, fiscal and monetary policy, and how foreign exchange rates affect GDP/NI,

The instruments and processes that shape the money supply including the money multiplier and the role of central banks, and their impact on inflation.
Candidates should understand the following macroeconomic principles and how they relate to the business cycle:
The general accounting conventions and data sources used to track economic activity,

The simplified Keynesian model, without adjustments for changes in price level or money supply, as it applies to changes in GDP caused by changes in investment, government spending, and net exports,
The relationships of price level, money demand, total demand, and total supply under the Keynesian Model.

B. Interest Theory and Finance

Interest Theory
Candidates should have a practical knowledge of the theory of interest in both finite and continuous time. That knowledge should include how these concepts are used in the various annuity functions, and apply the concepts of present and accumulated value for various streams of cash flows as a basis for future use in: reserving, valuation, pricing, duration, asset/liability management, investment income, capital budgeting, and contingencies. Candidates should be able to perform present and accumulated value calculations using non-level interest rates.

Candidates should understand the following principles and applications of interest theory:

Accumulation function and special cases of simple and compound interest,

Nominal and effective interest and discount rates, and the force of interest-constant and varying,

Valuation of discrete and continuous streams of payments, including the case in which the interest conversion period differs from the payment period,

Determination of yield rates on investments, both portfolio and investment year methods, and the time required to accumulate a given amount or repay a given loan amount,

Application of interest theory to amortization of lump sums, fixed income securities, depreciation, mortgages, etc.

Candidates should be able to use annuity functions in a broad finance context.
Finance
Candidates should understand and be able to analyze financial statements including balance sheets, income statements, and statements of cash flow. Candidates should be able to calculate discounted cash flow, internal rate of return, present and future values of bonds and apply the dividend growth model and price/earnings ratios concept to valuing stocks.

Candidates must be able to assess financial performance using net present value and the payback, discounted payback models, internal rate of return and profitability index models. Candidates should be able to analyze statements and identify what should be discounted, what other factors should be considered, and possible interactions between models.

Candidates should understand the trade-off between risk and return, the implications of the efficient market theory to the valuation of securities, and be able to perform the following:

Apply measures of portfolio risk, analyze the effects of diversification, systematic and unsystematic risks. Calculate portfolio risk and analyze the impact of individual securities on portfolio risk.

Identify efficient portfolios and apply the CAPM to firm cost of capital measures.

value cash flows and analyze the certainty equivalent versus risk adjusted discount rates using assumptions for inflation, the term structure of interest rates and default risk correctly in their calculations.
Candidates should understand the following concepts and be able to use them to analyze financial structures:

Efficient markets and their effect on security prices,

Capital structure and the impact of financial leverage and long/short term financing policies on capital structure,

Sources of capital and the definitions of techniques for valuing basic options such as calls and puts.
Candidates should understand and be able to analyze financial performance by evaluating financial statements and financial ratios such as leverage, liquidity, profitability, market value ratios and analysis of accounting return versus economic return.

Candidates should understand and be able to apply the basic principles of option pricing theory including:

Black-Scholes formula,

Valuation of basic options.
Note: Concepts, principles and techniques needed for Course 2 are covered in the references listed below. Candidates and educators may use other references, but candidates should be very familiar with the notation, terminology and viewpoints espoused in the listed references.

Texts

† Principles of Corporate Finance (Seventh Edition), 2002, by Brealey, R.A. and Myers, S.C., Chapters 1, 4-22, and 29. [Candidates may also use the Sixth Edition, 2000. Chapters 1, 4-21 and 28.]

Price Theory and Application (Fifth Edition), 2002, by Landsburg, S.E., Chapters 1-5, 7-8, 9 (9.3 only), 10-11, and 14.

# Theory of Interest (Second Edition), 1991, by Kellison, S.G., Chapters 1-3 (exclude 3.6, 3.7, 3.8, 3.10), 4 (exclude 4.8), 5 (exclude 5.8-5.9), 6 (exclude 6.7-6.8), 7 (7.3-7.4 only), and 8 (8.5-8.7 only).

Study Notes
SNs for Courses 1-6 are available on our Web site in the Education and Examination area under "Study Notes/Information." Hard copies may be purchased by using the Study Note and Published Reference order form in the back of the printed catalog or on the "Study Notes/Information" Web page.

Code Title
2-05-03# Course 2 Introductory Study Note
Tables for the Course 2 Examination
Theory of Interest Textbook Errata
2-12-00 November 2000 Course/Exam 2
2-10-01 May 2001 Course/Exam 2
2-12-01 November 2001 Course/Exam 2
2-21-00 Macroeconomics (Third or Fourth Printing)

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goldenbin
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板凳

发表于 2003-11-9 12:16:50 |只看该作者

Course 3 – 精算模型
This course is jointly administered by the SOA and CAS.

The examination for this course consists of four hours of multiple-choice questions and is identical to CAS
Exam 3.

This course develops the candidate's knowledge of the theoretical basis of actuarial models and the application of those models to insurance and other financial risks. A thorough knowledge of calculus, probability and interest theory is assumed. A knowledge of risk management at the level of Course 1 is also assumed.

The candidate will be required to understand, in an actuarial context, what is meant by the word "model," how and why models are used, their advantages and their limitations. The candidate will be expected to understand what important results can be obtained from these models for the purpose of making business decisions, and what approaches can be used to determine these results.

A variety of tables will be provided to the candidate in the study note package and at the examination. These include values for the standard normal distribution, illustrative life tables, and abridged inventories of discrete and continuous probability distributions. These tables are also available on the SOA and CAS Web sites. Since they will be included with the examination, candidates will not be allowed to bring copies of the tables into the examination room.

Learning Objectives
Understanding Actuarial Models
The candidate is expected to understand the models and techniques listed below and to be able to apply them to solve problems set in a business context. The effects of regulations, laws, accounting practices and competition on the results produced by these models are not considered in this course. The candidate is expected to be able to:

Explain what a mathematical model is and, in particular, what an actuarial model can be.

Discuss the value of building models for such purposes as: forecasting, estimating the impact of making changes to the modeled situation, estimating the impact of external changes on the modeled situation.

Identify the models and methods available, and understand the difference between the models and the methods.

Explain the difference between a stochastic and a deterministic model and identify the advantages/disadvantages of each.

Understand that all models presented (e.g., survival models, stochastic processes, aggregate loss models) are closely related.

Formulate a model for the present value, with respect to an assumed interest rate structure, of a set of future contingent cash flows. The model may be stochastic or deterministic.

Determine the characteristics of the components and the effects of changes to the components of the model in 6. Components include:

a deterministic interest rate structure;

a scheme for the amounts of the cash flows;

a probability distribution of the times of the cash flows; and

the probability distribution of the present value of the set of cash flows.
Apply a principle to a present value model to associate a cost or pattern of costs (possibly contingent) with a set of future contingent cash flows.

Principles include: equivalence, exponential, standard deviation, variance, and percentile.

Models include: present value models based on 9-12 below.

Applications include: insurance, health care, credit risk, environmental risk, consumer behavior (e.g., subscriptions), and warranties.
Characterize discrete and continuous univariate probability distributions for failure time random variables in terms of the life table functions, lx, qx, px, nqx, npx, and m|nqx, the cumulative distribution function, the survival function, the probability density function and the hazard function (force of mortality), as appropriate.

Establish relations between the different functions.

Develop expressions, including recursion relations, in terms of the functions for probabilities and moments associated with functions of failure time random variables, and calculate such quantities using simple failure time distributions.

Express the impact of explanatory variables on a failure time distribution in terms of proportional hazards and accelerated failure time models.
Given the joint distribution of two failure times:

Calculate probabilities and moments associated with functions of these random variables.

Characterize the distribution of the smaller failure time (the joint life status) and the larger failure time (the last survivor status) in terms of functions analogous to those in 9, as appropriate.

Develop expressions, including recursion relations, for probabilities and moments of functions of the joint life status and the last survivor status, and express these in terms of the univariate functions in 9 in the case in which the two failure times are independent.

Characterize the joint distribution of two failure times, the joint life status and the last survivor status using the common shock model.
Characterize the joint distribution (pdf and cdf) of the time until failure and the cause of failure in the competing risk (multiple decrement) model, in terms of the functions

Establish relations between the functions.

Given the joint distribution of the time of failure and the cause of failure, calculate probabilities and moments associated with functions of these random variables.

Apply assumptions about the pattern of failures between integral ages to obtain the associated (discrete) single decrement models from a discrete multiple decrement model as well as the discrete multiple decrement model that results from two or more discrete single decrement models.
Generalize the models of 9, 10, and 11 to multiple state models characterized in terms of transition probability functions or transition intensity functions (forces of transition).

Define a counting distribution (frequency distribution).

Characterize the following distributions in terms of their parameters and moments: Poisson, mixed Poisson, negative binomial, and binomial distributions.

Identify the applications for which these distributions are used and the reasons why they are used.

Given the parameters of a distribution, apply the distribution to an application.
Define a loss distribution.

Characterize the following families of distributions in terms of their parameters and moments: transformed beta, transformed gamma, inverse transformed gamma, lognormal and inverse Gaussian.

Apply the following techniques for creating new families of distributions: multiplication by a constant, raising to a power, exponentiation, and mixing.

Identify the applications in which these distributions are used and the reasons why they are used.

Given the parameters of a distribution, apply the distribution to an application.
Define a compound distribution.

Calculate probabilities associated with a compound distribution when the compounding distribution is a member of the families in 13, and the compounded distribution is discrete or a discretization of a continuous distribution.

Adjust the calculation of 16 for the impact of policy modifications such as deductibles, policy limits and coinsurance.

Define a stochastic process and distinguish between discrete-time and continuous-time processes.

Characterize a discrete-time Markov chain in terms of the transition probability matrix.

Use the Chapman-Kolmogorov equations to obtain probabilities associated with a discrete-time Markov chain.

Classify the states of a discrete-time Markov chain.

Calculate the limiting probabilities of a discrete-time Markov chain.
Define a counting process.

Characterize a Poisson process in terms of:

the distribution of the waiting times between events,

the distribution of the process increments,

the behavior of the process over an infinitesimal time interval.
Define a nonhomogeneous Poisson process.

Calculate probabilities associated with numbers of events and time periods of interest.
Define a compound Poisson process.

Calculate moments associated with the value of the process at a given time.

Characterize the value of the process at a given time as a compound Poisson random variable.
Define a Brownian motion process.

Determine the distribution of the value of the process at any time.

Determine the distribution of a hitting time.

Calculate the probability that one hitting time will be smaller than another.

Define a Brownian motion process with drift and a geometric Brownian motion process.
For a discrete-time surplus process:

Calculate the probability of ruin within a finite time by a recursion relation.

Analyze the probability of ultimate ruin via the adjustment coefficient and establish bounds.
For a continuous-time Poisson surplus process:

Derive an expression for the probability of ruin assuming that the claim amounts are combinations of exponential random variables.

Calculate the probability that the surplus falls below its initial level, determine the deficit at the time this first occurs, and characterize the maximal aggregate loss as a compound geometric random variable.

Approximate the probability of ruin using the compound geometric recursion.

Analyze the probability of ruin: analytically (e.g., adjustment coefficient); numerically; and by establishing bounds.

Determine the characteristics of the distribution of the amount of surplus (deficit) at: first time below the initial level; and the lowest level (maximal aggregate loss).
Analyze the impact of reinsurance on the probability of ruin and the expected maximum aggregate loss of a surplus process.

Generate discrete random variables using basic simulation methods.

Generate continuous random variables using basic simulation methods.

Construct an algorithm to appropriately simulate outcomes under a stochastic model.

Applications of Actuarial Models
The candidate is expected to be able to apply the models above to business applications. The
candidate should be able to determine an appropriate model for a given business problem and be
able to determine quantities that are important in making business decisions, given the values of the
model parameters. Relevant business applications include, but are not limited to:

Premium (rate) for life insurance and annuity contracts,

Premium (rate) for accident and health insurance contracts,

Premium (rate) for casualty (liability) insurance contracts,

Premium (rate) for property insurance contracts,

Rates for coverages under group benefit plans,

Loss reserves for insurance contracts,

Benefit reserves for insurance contracts,

Resident fees for Continuing Care Retirement Communities (CCRCs),

Cost of a warranty for manufactured goods,

Value of a financial instrument such as: a loan, a stock, an option, etc.,

Risk classification,

Solvency (ruin).
Note: Concepts, principles and techniques needed for Course 3 are covered in the references listed below. Candidates and professional educators may use other references, but candidates should be very familiar with the notation and terminology used in the listed references.

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goldenbin
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地板

发表于 2003-11-9 12:18:07 |只看该作者

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kenwind
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5楼

发表于 2003-11-10 01:26:19 |只看该作者

ASA前四门考试包括内容如下:

COURSE 1 : 微积分, 概率论.
COURSE 2:  微观经济学, 宏观经济学, 利息理论, 公司财务
COURSE 3:  精算数学, 风险理论和损失模型, 模拟( SIMULATION) , 随机过程.
COURSE 4:  计量经济, 生存模型, CREDIBILITY.

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