精算师考试攻略

Faculty of ActuariesInstitute of Actuaries

EXAMINATIONS

7 September 2001 (pm)

Subject 102 — Financial Mathematics

Time allowed: Three hours

INSTRUCTIONS TO THE CANDIDATE

1.Write your surname in full, the initials of your other names and your

Candidate’s Number on the front of the answer booklet.

2.Mark allocations are shown in brackets.

3.Attempt all 12 questions, beginning your answer to each question on a

separate sheet.

Graph paper is not required for this paper.

AT THE END OF THE EXAMINATION

Hand in BOTH your answer booklet and this question paper.

In addition to this paper you should have available

Actuarial Tables and an electronic calculator.

ã Faculty of Actuaries

102—S2001 (13.3.01)ã Institute of Actuaries1A 91-day government bill provides the purchaser with an annual effective rate of

return of 5%. Determine the annual simple discount rate at which the bill is

2021精算师资格考试中国精算师《经济学基础》考试指南

中国精算师资格《经济学基础》考试指南（大纲）解读

第一部分 考试指定教材与考试指南（大纲）解读

一、考试指定教材（中国精算师协会组编，刘澜飚主编，中国财政经济出版社出版）：

根据中国精算师资格考试指南规定，经济学基础科目指定教材为：中国精算师资格考试用书《经济学基础》，2010年版，所有章节全部内容。

二、考试相关情况简介

1考试时间：3小时

2考试题型：

3考试要求：

通过本科目的学习，考生应该掌握现代经济学和金融学的基本概念、基本方法和原理。本科目的学习将帮助学员掌握和运用经济学、金融学中一定的定性分析和定量分析方法，初步具备较宽的专业知识面和较强的分析问题和解决问题的能力。

三、经济学基础考试指南解读

1微观经济学（分数比例约为50%） 考生在掌握微观经济学基本原理的基础上，能够通过建立模型的方法了解经济事件的结构并对基本的经济活动进行分析；增加对市场和经济决策行为的理解。

（1）供给和需求理论，市场均衡价格理论

这部分内容涉及到教材第二章，一共包括四节内容：需求分析、供给分析、均衡价格、弹性分析以及政府干预的效用。这部分内容属于基础性内容，较为容易。其中，需求价格弹性、需求收入弹性、需求交叉价格弹性和政府对市场的干预（最高限价、最低限价）是考试的重点，蛛网模型的分析是考试的难点，对于三种蛛网类型应熟练的掌握。

（2）消费者行为理论

这部分内容涉及到教材第三章，一共包括两节内容：消费者均衡和不确定条件下的消费者选择。本章属于重要考试内容，各种题型都出现过。第一节中，按照序数效用论的观点，结合无差异曲线和预算线来分析消费者均衡（易出计算题）。还利用比较静态分析来分析当价格、货币收入发生变化时的影响，从而推导得出恩格尔曲线和需求曲线。无差异曲线、替代效应、收入效应、消费者剩余这些概念一定要熟练掌握。第二节研究不确定情况下消费者的选择，按照消费者对风险的偏好程度分为三种类型（风险偏好、风险规避和风险中性）。另外，风险贴水这个概念要掌握。

希望对大家有所帮助，多谢您的浏览！

中国精算师资格考试用书《数学》

第1章 随机事件与概率

第2章 随机变量与分布函数

第3章 随机变量的数字特征

第4章 大数定律与中心极限定理

第5章 统计量及其分布

第6章 参数估计

第7章 假设检验

第8章 常用统计方法

第9章 时间序列分析

第10章 随机过程的基本概念和基本类型 （补一下随机过程）

第11章 几种常用的随机过程

第12章 随机微积分

中国精算师资格考试用书《金融数学》

第一篇 利息理论

第1章 利息的基本概念

第2章 年金

第3章 收益率

第4章 债务偿还

第5章 债券及其定价理论

第二篇 利率期限结构与随机利率模型

第6章 利率期限结构理论

第7章 随机利率模型

第三篇 金融衍生工具定价理论

第8章 金融衍生工具介绍

第9章 金融衍生工具定价理论

第四篇 投资组合理论

第10章 投资组合理论

第11章 CAPM和APT

中国精算师资格考试用书《精算模型》

第1章 绪论

第一篇 基本风险模型

第2章 生存分析的基本函数及生存模型

第3章 生命表

第4章 理赔额和理赔次数的分布

第5章 短期个体风险模型

第6章 短期聚合风险模型希望对大家有所帮助，多谢您的浏览！

第7章 破产模型

第二篇 模型的估计和选择

第8章 经验模型

第9章 参数模型的估计

第10章 参数模型的检验和选择

第三篇 模型的调整和随机模拟

第11章 修匀理论

第12章 信度理论

中国精算师资格考试用书《经济学》

第一篇 微观经济学

第1章 经济学的研究对象和研究方法

第2章 市场机制

第3章 消费者行为理论

第4章 生产者行为理论

第5章 市场结构理论

第6章 要素市场与收入分配理论

第7章 一般均衡与效率

第8章 市场失灵和微观经济政策

第二篇 宏观经济学

第9章 国民收入核算原理与结构

November 2001Course 2Interest Theory, Economics and FinanceSociety of Actuaries/Casualty Actuarial SocietyCourse 2, November 200121.Ernie makes deposits of 100 at time 0, and X at time 3 . The fund grows at a force ofinterest 2100ttδ=, t > 0 .The amount of interest earned from time 3 to time 6 is X.Calculate X.(A)385(B)485(C)585(D)685(E)785Course 2, November 200132.The production of a good requires two inputs, labor and capital. At its current level ofdaily output, a competitive firm employs 100 machine hours of capital and 200 laborhours. The marginal product of machine hours is 10 units. The marginal product of laborhours is 5 units. The rental rate, or “price,” of capital is 20 per machine hour.If the firm minimizes its costs, what is the hourly wage rate?(A) 2.5(B) 5.0(C)10.0(D)20.0(E)40.0Course 2, November st year, a country's output increased 2.6%. The country’s capital stock increased 4.0%while its labor hours increased 2.0%. The labor share of total income was 70%.What was the country’s total factor productivity growth last year?(A)–0.8(B) 0.0(C) 2.3(D) 5.2(E) 6.0Course 2, November 200154.Consider a project lasting one year. The initial outlay is 100,000 at the beginning of theyear and the expected inflow is 120,000 at the end of the year. The opportunity cost ofcapital for the project is 20%, the borrowing rate is 8%, and the marginal tax rate is 35%.Calculate the adjusted present value if the company borrows 54% of the project’srequired investment.(A) 800(B)1260(C)1400(D)3150(E)3500Course 2, November 200165.Mike buys a perpetuity-immediate with varying annual payments. During the first 5years, the payment is constant and equal to 10 . Beginning in year 6, the payments startto increase. For year 6 and all future years, the current year’s payment is K% larger thanthe previous year’s payment.At an annual effective interest rate of 9.2%, the perpetuity has a present value of 167.50 .Calculate K, given K < 9.2 .(A)4.0(B)4.2(C)4.4(D)4.6(E)4.8Course 2, November 200176.A 10-year loan of 2000 is to be repaid with payments at the end of each year.It can be repaid under the following two options:(i)Equal annual payments at an annual effective rate of 8.07% .(ii)Installments of 200 each year plus interest on the unpaid balanceat an annual effective rate of i .The sum of the payments under option (i) equals the sum of the payments underoption (ii) .Determine i .(A)8.75%(B)9.00%(C)9.25%(D)9.50%(E)9.75%Course 2, November 200187.The demand curve for Product X is steep, whereas the demand curve for Product Y is almost flat.The supply curves for the two products are identical. Equilibrium price and quantity are thesame for the two products. Consider a 5% excise tax on both products.Which of the following statements about the impact of the tax is FALSE?(A)Equilibrium quantity will decrease less for Product X than for Product Y .(B)Consumers face a larger price increase for Product X than for Product Y .(C)The tax burden experienced by producers is larger for Product Y than for Product X .(D)The government collects more taxes from Product Y than from Product X .(E)In each market, the economic incidence of the tax would be the same if the 5%excise tax were replaced by a 5% sales tax.Course 2, November 200198.A corporation is considering an investment in one of two potential projects. Each projectrequires an initial investment of 5000 .Project X will produce cash flows of 300 at the end of each 6-month period. The cashflows are expected to continue forever. The first cash flow is expected 6 months after theinitial investment.Project Y will have a single cash flow of Z, which will be received exactly 5 years afterthe initial investment.The IRR on both projects is the same.Calculate the profitability index on Project Y, using an annual effective interest rate of10% .(A) 8.5%(B) 9.4%(C)10.3%(D)11.2%(E)12.1%Course 2, November 2001109.A loan is amortized over five years with monthly payments at a nominal interest rate of9% compounded monthly. The first payment is 1000 and is to be paid one month fromthe date of the loan. Each succeeding monthly payment will be 2% lower than the priorpayment.Calculate the outstanding loan balance immediately after the 40th payment is made.(A)6751(B)6889(C)6941(D)7030(E)7344Course 2, November 20011110.Five self-interested colleagues are dining together at a restaurant where desserts cost 5.0each. If dining alone, one of the colleagues would be willing to pay 3.5 for a dessert.Two of the colleagues would be willing to pay 4.5 for a dessert while the other two wouldbe willing to pay 5.5 . The restaurant will not give individual checks, so the colleagueshave agreed to split the bill evenly.If the five colleagues each act out of their own self-interest, how many desserts will beordered?(A)0(B)2(C)3(D)4(E)5