北美精算师金融数学考试内容2013-04-exam-fm

Probability (機率論, 簡稱P)
3小時選擇題，共30題
二.

Financial Mathematics (財務數學, 簡稱 FM)
2.5小時選擇題，共30題
PE EXAMS(續)
三.
Actuarial Models (精算模型, 簡稱M)
1.
Life contingencies(壽險精算, 簡稱MLC)
MLC 及 MFE 心得分享
Exam M-Actuarial Models
分為MLC及MFE兩部分 MLC：Life Contingencies Segment MFE：Financial Economics Segment 考試時間及題數分別為
MLC-3小時，考30題選擇題 MFE-2.5小時，考25題選擇題(新制) 不必同時報考 每年只有Spring及Fall兩考試時段(五月，十 一月)
Exam MLC 準備心得
Life insurances and annuities 一開始接觸會因為太多符號要記，而覺得很難 入門，譬如： A 70 , a 40 :10 , 10 q 30 要能把握各種符號的形成邏輯，可以幫助記憶 要能夠求各種情況下以下類型隨機變數的 期望值變異數及百分位數： present-value-of-benefit random variables present-value-of-loss-at-issue random variables 要能活用Recursion法解題(熟悉每條公式之間的 代換關係)
3小時選擇題，共30題
2.
Financial Economics(財務經濟, 簡稱MFE)
2.5小時選擇題，約25題(2009新制，故不確定幾 題)

基本教育阶段(6门课程)：课程1：精算科学的数学基础说明：这门课程的目的是为了培养关于一些基础数学工具的知识，形成从数量角度评估风险的能力，特别是应用这些工具来解决精算科学中的问题。

并且假设学员在学习这门课程之前已经熟练掌握了微积分、概率论的有关内容及风险管理的基本知识。

主要内容及概念：微积分、概率论、风险管理（包括损失频率、损失金额、自留额、免赔额、共同保险和风险保费）课程2：利息理论、经济学和金融学说明：这门课程包括利息理论，中级微观经济学和宏观经济学，金融学基础。

在学习这门课程之前要求具有微积分和概率论的基础知识。

主要内容及概念：利息理论，微观经济学，宏观经济学，金融学基础课程3：随机事件的精算模型说明：通过这门课程的学习，培养学员关于随机事件的精算模型的基础知识及这些模型在保险和金融风险中的应用。

在学习这门课程之前要求熟练掌握微积分、概率论和数理统计的相关内容。

建议学员在通过课程1和课程2后学习这门课程。

主要内容及概念：保险和其它金融随机事件，生存模型，人口数据分析，定量分析随机事件的金融影响课程4：精算建模方法说明：该课程初步介绍了建立模型的基础知识和用于建模的重要的精算和统计方法。

在学习这门课程之前要求熟练掌握微积分、线性代数、概率论和数理统计的相关内容。

主要内容及概念：模型－模型的定义－为何及如何使用模型－模型的利弊－确定性的和随机性的模型－模型选择－输入和输出分析－敏感性检验－研究结果的检验和反馈方法－回归分析－预测－风险理论－信度理论课程5－精算原理应用说明：这门课程提供了产品设计，风险分类，定价/费率拟定/建立保险基金，营销，分配，管理和估价的学习。

覆盖的范围包括金融保障计划,职工福利计划，事故抚恤计划，政府社会保险和养老计划及一些新兴的应用领域如产品责任，担保的评估，环境的维护成本和制造业的应用。

该课程的学习材料综合了各种计划和覆盖范围以展示精算原理在各研究领域中应用的一致性和差异性。

ACTUARIES/CASUALTY ACTUARIAL SOCIETYOFSOCIETYEXAM FM FINANCIAL MATHEMATICSEXAM FM SAMPLE QUESTIONSCopyright 2005 by the Society of Actuaries and the Casualty Actuarial Society Some of the questions in this study note are taken from past SOA/CAS examinations.11/08/04 2U.S.A.FM-09-05INPRINTED11/08/04 3These questions are representative of the types of questions that might be asked of candidates sitting for the new examination on Financial Mathematics (2/FM). These questions are intended to represent the depth of understanding required of candidates. The distribution of questions by topic is not intended to represent the distribution of questions on future exams.11/08/04 41.Bruce deposits 100 into a bank account. His account is credited interest at a nominal rate of interest of 4% convertible semiannually.At the same time, Peter deposits 100 into a separate account. Peter’s account is credited interest at a force of interest of δ.After 7.25 years, the value of each account is the same.Calculate δ.0.0388(A)0.0392(B)0.0396(C)0.0404(D)0.0414(E)11/08/04 52.Kathryn deposits 100 into an account at the beginning of each 4-year period for 40 years. The account credits interest at an annual effective interest rate of i.The accumulated amount in the account at the end of 40 years is X, which is 5 times the accumulated amount in the account at the end of 20 years.Calculate X.4695(A)5070(B)5445(C)5820(D)6195(E)11/08/04 63.Eric deposits 100 into a savings account at time 0, which pays interest at a nominal rate of i, compounded semiannually.Mike deposits 200 into a different savings account at time 0, which pays simple interest at an annual rate of i.Eric and Mike earn the same amount of interest during the last 6 months of the 8th year.Calculate i.9.06%(A)9.26%(B)9.46%(C)9.66%(D)9.86%(E)11/08/04 74.John borrows 10,000 for 10 years at an annual effective interest rate of 10%. He can repay this loan using the amortization method with payments of 1,627.45 at the end of each year. Instead, John repays the 10,000 using a sinking fund that pays an annual effective interest rate of 14%. The deposits to the sinking fund are equal to 1,627.45 minus the interest on the loan and are made at the end of each year for 10 years.Determine the balance in the sinking fund immediately after repayment of the loan.2,130(A)2,180(B)2,230(C)2,300(D)2,370(E)11/08/04 85.An association had a fund balance of 75 on January 1 and 60 on December 31. At the end of every month during the year, the association deposited 10 from membership fees. There were withdrawals of 5 on February 28, 25 on June 30, 80 on October 15, and 35 on October 31.Calculate the dollar-weighted (money-weighted) rate of return for the year.(A) 9.0%(B) 9.5%10.0%(C)10.5%(D)11.0%(E)11/08/04 96.A perpetuity costs 77.1 and makes annual payments at the end of the year.The perpetuity pays 1 at the end of year 2, 2 at the end of year 3, …., n at the endof year (n+1). After year (n+1), the payments remain constant at n. The annual effective interest rate is 10.5%.Calculate n.17(A)18(B)19(C)20(D)21(E)11/08/04 107.1000 is deposited into Fund X, which earns an annual effective rate of 6%. At the end of each year, the interest earned plus an additional 100 is withdrawn from the fund. At the end of the tenth year, the fund is depleted.The annual withdrawals of interest and principal are deposited into Fund Y, which earns an annual effective rate of 9%.Determine the accumulated value of Fund Y at the end of year 10.1519(A)1819(B)2085(C)2273(D)2431(E)11/08/04 1111/08/04128.You are given the following table of interest rates: Calendar Year of Original Investment Investment Year Rates (in %) PortfolioRates(in %) yi 1y i 2y i 3y i 4y i 5y i y +5 1992 8.25 8.25 8.4 8.5 8.5 8.351993 8.5 8.7 8.75 8.9 9.0 8.61994 9.0 9.0 9.1 9.1 9.2 8.851995 9.0 9.1 9.2 9.3 9.4 9.11996 9.25 9.35 9.5 9.55 9.6 9.351997 9.5 9.5 9.6 9.7 9.71998 10.0 10.0 9.9 9.81999 10.0 9.8 9.72000 9.5 9.52001 9.0A person deposits 1000 on January 1, 1997. Let the following be the accumulated value of the 1000 on January 1, 2000:P :under the investment year method Q :under the portfolio yield method R : where the balance is withdrawn at the end of everyyear and is reinvested at the new money rateDetermine the ranking of P , Q , and R .(A)P Q R >> (B) P R Q >>(C) Q P R >>(D) R P Q >>(E)R Q P >>9.A 20-year loan of 1000 is repaid with payments at the end of each year.Each of the first ten payments equals 150% of the amount of interest due. Each of the last ten payments is X.The lender charges interest at an annual effective rate of 10%.Calculate X.(A) 32(B) 57(C) 70(D) 97(E)11711/08/04 1310.A 10,000 par value 10-year bond with 8% annual coupons is bought at a premiumto yield an annual effective rate of 6%.Calculate the interest portion of the 7th coupon.632(A)642(B)651(C)660(D)(E)66711/08/04 1411.A perpetuity-immediate pays 100 per year. Immediately after the fifth payment, the perpetuity is exchanged for a 25-year annuity-immediate that will pay X at the end of the first year. Each subsequent annual payment will be 8% greater than the preceding payment.The annual effective rate of interest is 8%.Calculate X.54(A)64(B)74(C)84(D)94(E)11/08/04 1512.Jeff deposits 10 into a fund today and 20 fifteen years later. Interest is credited at a nominal discount rate of d compounded quarterly for the first 10 years, and at a nominal interest rate of 6% compounded semiannually thereafter. The accumulated balance in the fund at the end of 30 years is 100.Calculate d.4.33%(A)4.43%(B)4.53%(C)4.63%(D)4.73%(E)11/08/04 1611/08/041713.Ernie makes deposits of 100 at time 0, and X at time 3. The fund grows at a force of interest2100t t δ=, t > 0.The amount of interest earned from time 3 to time 6 is also X .Calculate X .(A) 385(B) 485(C) 585(D) 685(E) 78514.Mike buys a perpetuity-immediate with varying annual payments. During the first 5 years, the payment is constant and equal to 10. Beginning in year 6, the payments start to increase. For year 6 and all future years, the current year’s payment is K% larger than the previous year’s payment.At an annual effective interest rate of 9.2%, the perpetuity has a present value of167.50.Calculate K, given K < 9.2.4.0(A)4.2(B)4.4(C)4.6(D)4.8(E)11/08/04 1815.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 balance at an annual effective rate of i.The sum of the payments under option (i) equals the sum of the payments under option (ii).Determine i.8.75%(A)9.00%(B)9.25%(C)9.50%(D)9.75%(E)11/08/04 1916.A loan is amortized over five years with monthly payments at a nominal interest rate of 9% compounded monthly. The first payment is 1000 and is to be paid one month from the date of the loan. Each succeeding monthly payment will be 2% lower than the prior payment.Calculate the outstanding loan balance immediately after the 40th payment is made.6751(A)6889(B)6941(C)7030(D)7344(E)11/08/04 2017.To accumulate 8000 at the end of 3n years, deposits of 98 are made at the end of each of the first n years and 196 at the end of each of the next 2n years.The annual effective rate of interest is i. You are given (l + i)n = 2.0.Determine i.11.25%(A)11.75%(B)12.25%(C)12.75%(D)13.25%(E)11/08/04 2118.Olga buys a 5-year increasing annuity for X.Olga will receive 2 at the end of the first month, 4 at the end of the second month, and for each month thereafter the payment increases by 2.The nominal interest rate is 9% convertible quarterly.Calculate X.2680(A)2730(B)2780(C)2830(D)2880(E)11/08/04 2219.You are given the following information about the activity in two different investment accounts:Account KFundvalue ActivityWithdrawal Date beforeactivity DepositJanuary 1, 1999 100.0July 1, 1999 125.0 XOctober 1, 1999 110.0 2XDecember 31, 1999 125.0Account Lvalue ActivityFundactivity DepositWithdrawal Date beforeJanuary 1, 1999 100.0July 1, 1999 125.0 XDecember 31, 1999 105.8During 1999, the dollar-weighted (money-weighted) return for investment account K equals the time-weighted return for investment account L, which equals i.Calculate i.10%(A)12%(B)(C)15%11/08/04 23(D)18%20%(E)11/08/04 2420.David can receive one of the following two payment streams:(i) 100 at time 0, 200 at time n, and 300 at time 2n(ii) 600 at time 10At an annual effective interest rate of i, the present values of the two streams are equal.Given v n = 0.76, determine i.3.5%(A)4.0%(B)4.5%(C)5.0%(D)5.5%(E)11/08/04 2521.Payments are made to an account at a continuous rate of (8k + tk), where010t≤≤ .Interest is credited at a force of interest δt =18t+.After 10 years, the account is worth 20,000.Calculate k.(A)111(B)116(C)121(D)126(E)13111/08/04 2622.You have decided to invest in Bond X, an n-year bond with semi-annual coupons and the following characteristics:• Par value is 1000.• The ratio of the semi-annual coupon rate to the desired semi-annual yield rate,ri, is 1.03125.• The present value of the redemption value is 381.50.Given v n = 0.5889, what is the price of bond X?(A)1019(B)1029(C)1050(D)1055(E)107211/08/04 2723.Project P requires an investment of 4000 at time 0. The investment pays 2000 at time 1 and 4000 at time 2.Project Q requires an investment of X at time 2. The investment pays 2000 at time 0 and 4000 at time 1.The net present values of the two projects are equal at an interest rate of 10%.Calculate X.5400(A)5420(B)5440(C)5460(D)5480(E)11/08/04 2824.A 20-year loan of 20,000 may be repaid under the following two methods:i) amortization method with equal annual payments at an annual effectiverate of 6.5%ii) sinking fund method in which the lender receives an annual effectiverate of 8% and the sinking fund earns an annual effective rate of jBoth methods require a payment of X to be made at the end of each year for 20 years. Calculate j.(A) j≤ 6.5%j≤ 8.0%<6.5%(B)<j≤ 10.0%8.0%(C)<j≤ 12.0%10.0%(D)(E) j > 12.0%11/08/04 2925.A perpetuity-immediate pays X per year. Brian receives the first n payments, Colleen receives the next n payments, and Jeff receives the remaining payments. Brian's share of the present value of the original perpetuity is 40%, and Jeff's share is K.Calculate K.24%(A)28%(B)32%(C)36%(D)40%(E)11/08/04 3026.Seth, Janice, and Lori each borrow 5000 for five years at a nominal interest rate of 12%, compounded semi-annually.Seth has interest accumulated over the five years and pays all the interest and principal in a lump sum at the end of five years.Janice pays interest at the end of every six-month period as it accrues and the principal at the end of five years.Lori repays her loan with 10 level payments at the end of every six-month period.Calculate the total amount of interest paid on all three loans.8718(A)(B)87288738(C)8748(D)(E)875811/08/04 3111/08/04 3227.Bruce and Robbie each open up new bank accounts at time 0. Bruce deposits 100 into his bank account, and Robbie deposits 50 into his. Each account earns the same annual effective interest rate.The amount of interest earned in Bruce's account during the 11th year is equal to X. The amount of interest earned in Robbie's account during the 17th year is also equal to X.Calculate X.28.0(A)31.3(B)34.6(C)36.7(D)38.9(E)11/08/04 3311/08/043428.Ron is repaying a loan with payments of 1 at the end of each year for n years. The amount of interest paid in period t plus the amount of principal repaid in period t + 1 equals X .Calculate X .(A)1 + n t v i − (B)1 + n t v d − (C)1 + v n −t i (D)1 + v n −t d (E)1+ v n −t29.At an annual effective interest rate of i, i > 0%, the present value of a perpetuity paying `10 at the end of each 3-year period, with the first payment at the end of year 3, is 32.At the same annual effective rate of i, the present value of a perpetuity paying 1 at the end of each 4-month period, with first payment at the end of 4 months, is X.Calculate X.31.6(A)32.6(B)33.6(C)34.6(D)35.6(E)11/08/04 3530.As of 12/31/03, an insurance company has a known obligation to pay $1,000,000 on 12/31/2007. To fund this liability, the company immediately purchases 4-year 5% annual coupon bonds totaling $822,703 of par value. The company anticipates reinvestment interest rates to remain constant at 5% through 12/31/07. The maturity value of the bond equals the par value.Under the following reinvestment interest rate movement scenarios effective 1/1/2004, what best describes the insurance company’s profit or (loss) as of 12/31/2007 after the liability is paid?InterestRates Dropby ½% Interest Rates Increase by ½%(A) +6,606 +11,147(B) (14,757) +14,418(C) (18,911) +19,185(D) (1,313) +1,32311/08/04 36(E) Breakeven Breakeven11/08/04 3731.An insurance company has an obligation to pay the medical costs for a claimant. Average annual claims costs today are $5,000, and medical inflation is expected to be 7% per year. The claimant is expected to live an additional 20 years.Claim payments are made at yearly intervals, with the first claim payment to be made one year from today.Find the present value of the obligation if the annual interest rate is 5%.(A) 87,932(B) 102,514(C) 114,611(D) 122,634(E) Cannot be determined11/08/04 3832.An investor pays $100,000 today for a 4-year investment that returns cash flows of $60,000 at the end of each of years 3 and 4. The cash flows can be reinvested at 4.0% per annum effective.If the rate of interest at which the investment is to be valued is 5.0%, what is the net present value of this investment today?(A) -1398(B) -699(C) 699(D) 1398(E) 2,62911/08/04 3933.You are given the following information with respect to a bond:par amount: 1000term to maturity 3 yearsannual coupon rate 6% payable annuallyTerm Annual Spot InterestRates1 7%2 8%3 9%Calculate the value of the bond.(A) 906(B) 926(C) 930(D) 950(E) 100011/08/04 4011/08/04 4134.You are given the following information with respect to a bond:par amount: 1000term to maturity 3 yearsannual coupon rate 6% payable annuallyTerm Annual Spot InterestRates1 7%2 8%3 9%Calculate the annual effective yield rate for the bond if the bond is sold at a price equal to its value.(A) 8.1%(B) 8.3%(C) 8.5%(D) 8.7%11/08/04 42(E) 8.9%11/08/04 4335.The current price of an annual coupon bond is 100. The derivative of the price of the bond with respect to the yield to maturity is -700. The yield to maturity is an annual effective rate of 8%.Calculate the duration of the bond.(A) 7.00(B) 7.49(C) 7.56(D) 7.69(E) 8.0011/08/04 4436.Calculate the duration of a common stock that pays dividends at the end of each year into perpetuity. Assume that the dividend is constant, and that the effective rate of interest is 10%.(A) 7(B) 9(C) 11(D) 19(E) 2711/08/04 4537.Calculate the duration of a common stock that pays dividends at the end of each year into perpetuity. Assume that the dividend increases by 2% each year and that the effective rate of interest is 5%.(A) 27(B) 35(C) 44(D) 52(E) 5811/08/04 4638. – 44. skipped11/08/04 5245.You are given the following information about an investment account:ImmediatelyDate ValueDepositBefore DepositJanuary 1 10July 1 12 XXDecember31Over the year, the time-weighted return is 0%, and the dollar-weighted (money-weighted) return is Y.Calculate Y.(A) -25%(B) -10%(C) 0%(D) 10%11/08/04 53(E) 25%11/08/04 5446.Seth borrows X for four years at an annual effective interest rate of 8%, to be repaid with equal payments at the end of each year. The outstanding loan balance at the end of the third year is 559.12.Calculate the principal repaid in the first payment.(A) 444(B) 454(C) 464(D) 474(E) 48411/08/04 5547.Bill buys a 10-year 1000 par value 6% bond with semi-annual coupons. The price assumes a nominal yield of 6%, compounded semi-annually.As Bill receives each coupon payment, he immediately puts the money into an account earning interest at an annual effective rate of i.At the end of 10 years, immediately after Bill receives the final coupon payment and the redemption value of the bond, Bill has earned an annual effective yield of 7% on his investment in the bond.Calculate i.(A) 9.50%(B) 9.75%(C) 10.00%(D) 10.25%(E) 10.50%11/08/04 56。

北美精算师科目
北美精算师是指在北美洲国家（如美国和加拿大）考取精算师资格的人员。

北美精算师的资格考试主要由精算师协会（如美国精算师协会和加拿大精算师协会）负责组织和管理。

在北美洲，精算师的考试科目一般包括以下几个方面：
1. 初级精算师考试（Pre-Associate Level Examinations）：通常
包括5门考试科目，涵盖基础数学、概率与统计、金融数学、经济学和精算原理等方面的知识。

2. 候选精算师考试（Associate Level Examinations）：通常包
括7门考试科目，涵盖资本市场、保险经济学、保险精算理论、统计方法和风险模型等方面的知识。

3. 精算师考试（Fellow Level Examinations）：通常包括8门
考试科目，涵盖保险精算模型、企业风险管理、保险产品设计、保险会计和保险经营战略等方面的知识。

根据考试进度和个人兴趣，考生可以选择逐步完成以上不同级别的考试。

完成所有考试科目并满足相关经验要求后，考生将获得北美精算师资格认证。

值得注意的是，具体的考试科目和要求可能会因精算师协会的不同而有所差异，因此考生在报考前应详细了解并遵循相应的规定和要求。

ASA的课程课程1：精算科学的数学基础(MathematicalfoundationsofActuarialScience)这门课程的目的是为了培养关于一些基础数学工具的知识，形成从数量角度评估风险的能力，特别是应用这些工具来解决精算科学中的问题。

主要内容及概念：微积分、概率论、风险管理（包括损失频率、损失金额、自留额、免赔额、共同保险和风险保费）。

课程2：利息理论，经济与金融(InterestTheory，EconomicsandFinance)这门课程包括利息理论，中级微观经济学和宏观经济学，金融学基础。

课程3：关于风险的精算模型(ActuaricalModels)通过这门课程的学习，培养学员关于随机事件的精算模型的基础知识及这些模型在保险和金融风险中的应用。

主要内容包括：保险和其它金融随机事件，生存模型，人口数据分析，定量分析随机事件的金融影响。

课程4：精算建模方法（ActuarialModeling）该课程初步介绍了建立模型的基础知识和用于建模的重要的精算和统计方法。

主要内容包括：为何及如何选择和使用模型，回归分析，风险理论和信用理论。

课程5：基本精算原理的应用(ApplicationofBasicActuarialPrinciples)这门课程提供了产品设计，风险分类，定价/费率拟定/建立保险基金，营销，分配，管理和估价的学习。

覆盖的范围包括金融保障计划,职工福利计划，事故抚恤计划，政府社会保险和养老计划及一些新兴的应用领域如产品责任，担保的评估，环境的维护成本和制造业的应用。

课程6：金融与投资(FinanceandInvestments)该课程是用于投资和资产负债管理领域的精算原理的拓展。

学员在完成该课程的学习后，将会对资本市场、投资工具、衍生证券及应用、投资组合管理和资产－负债管理有深入的了解。

主要内容及概念：资本市场和基本投资原理，投资工具，衍生证券，投资组合管理的原理，资产负债管理。

016*.高级非寿险精算实务
017*.团体保险 018*.意外伤害和健康保险 019*.投资学 020*.养老金计划
A S A R U C
Actuarial Student Association at RUC







1.精算数学基础 概率论 P 2.金融数学 FM 3.精算模型 MLC/MFE 4.精算建模方法 C 5.VEE 统计，经济，财务 6.FAP 实务 7.CERA(ERM,FSA module) 高级精算实务—金融经济理论 DP.高级精算实务—团体人寿险；个人和团体健康险设计定价 DP.高级精算实务—个险，年金设计定价(北美，加拿大) Advanced Portfolio Management CSP养老金计划美国,加拿大 CSP个人和团体健康险设计定价美国加拿大 Decision Making and Communication (DMAC) Module Fellowship Admissions Course (FAC)

折扣申请


考试时间(P：2、3、7、9、11月；FM-C：5、11月)
各科目的准备时间


评分方式 （10分制）
计算器
BA-35、BA II Plus、TI-30X、TI-30Xa、TI-30XIIS、TI-30XIIB
中国人民大学学生精算协会
2.金融数学 FM 3.精算模型 MLC/MFE
4.精算建模方法 C 5.VEE 统计，经济，财务 6.FAP 实务 7.CERA(ERM,FSA module) 高级精算实务—金融经济理论 DP.高级精算实务—团体人寿险； 个人和团体健康险设计定价 DP.高级精算实务—个险，年金设 计定价(北美，加拿大) Advanced Portfolio Management CSP养老金计划美国,加拿大

北美精算师报考指南◇ 考试介绍在北美，精算师可以分为两类：寿险精算师和财产意外险精算师。

寿险精算师处理的是与人的生命相关的精算领域例如人寿保险、健康保险、养老金，寿险精算师参加的是北美精算师考试(SOA)。

财产意外险精算师处理非寿险的精算领域如车险、火险、水险、信用险，这一类别的考试叫做北美财产意外险精算师考试(CAS)。

本报考指南主要介绍北美精算师考试(SOA)，关于北美财产意外险精算师考试(CAS)可阅读：北美财产意外险精算师考试介绍。

北美精算师协会(SOA)是一个以服务于公众和学会会员为目标而建立的教育、研究和专业性组织。

其任务是发展精算知识，加强精算师向金融和社会涉及的未来不确定问题提供专业建议以及解决方法的能力。

北美精算师协会的考试有：准精算师(ASA)、注册企业风险分析员(CERA)、精算师(FSA)。

SOA自1987年起与我国南开大学合作设立了精算教育培训项目，并于1992年在南开设立考试中心。

目前，SOA在北京、上海、天津、长沙、合肥、深圳、西安、广州共设有8个考试中心。

附：北美精算师资格考试相关法律条规北美精算师资格考试规则Exam Rules and Regulations/Instructions to Candidates北美精算师资格考试网络教学课程条款及细则Society of Actuaries T erms and Conditions Agreement for e-Learning Candidates◇ 报名条件北美精算师考试原则上无明确的报考学历等要求，但VEE学分豁免需SOA认可的大学或研究所的学习证明。

VEE课程学分也可通过SOA的网上教学来获得。

◇ 报名时间通常所说的考试为初级考试(preliminary examinations)部分，北美精算师初级考试每年各科目考试次数及报名时间都不相同。

2013年各科目报名截止时间见：2013年北美精算师初级考试时间表。

基本教育阶段(6门课程)：课程1：精算科学的数学基础说明：这门课程的目的是为了培养关于一些基础数学工具的知识，形成从数量角度评估风险的能力，特别是应用这些工具来解决精算科学中的问题。

并且假设学员在学习这门课程之前已经熟练掌握了微积分、概率论的有关内容及风险管理的基本知识。

主要内容及概念：微积分、概率论、风险管理（包括损失频率、损失金额、自留额、免赔额、共同保险和风险保费）课程2：利息理论、经济学和金融学说明：这门课程包括利息理论，中级微观经济学和宏观经济学，金融学基础。

在学习这门课程之前要求具有微积分和概率论的基础知识。

主要内容及概念：利息理论，微观经济学，宏观经济学，金融学基础课程3：随机事件的精算模型说明：通过这门课程的学习，培养学员关于随机事件的精算模型的基础知识及这些模型在保险和金融风险中的应用。

在学习这门课程之前要求熟练掌握微积分、概率论和数理统计的相关内容。

建议学员在通过课程1和课程2后学习这门课程。

主要内容及概念：保险和其它金融随机事件，生存模型，人口数据分析，定量分析随机事件的金融影响课程4：精算建模方法说明：该课程初步介绍了建立模型的基础知识和用于建模的重要的精算和统计方法。

在学习这门课程之前要求熟练掌握微积分、线性代数、概率论和数理统计的相关内容。

主要内容及概念：模型－模型的定义－为何及如何使用模型－模型的利弊－确定性的和随机性的模型－模型选择－输入和输出分析－敏感性检验－研究结果的检验和反馈方法－回归分析－预测－风险理论－信度理论课程5－精算原理应用说明：这门课程提供了产品设计，风险分类，定价/费率拟定/建立保险基金，营销，分配，管理和估价的学习。

覆盖的范围包括金融保障计划,职工福利计划，事故抚恤计划，政府社会保险和养老计划及一些新兴的应用领域如产品责任，担保的评估，环境的维护成本和制造业的应用。

该课程的学习材料综合了各种计划和覆盖范围以展示精算原理在各研究领域中应用的一致性和差异性。

精算师考试内容数学考试时间：3小时考试形式：选择题考试要求：本科目是关于风险管理和精算中随机数学的基础课程。

通过本科目的学习，考生应该掌握基本的概率统计知识，具备一定的数据分析能力，初步了解各种随机过程的性质。

考生应掌握概率论、统计模型和应用随机过程的基本概念和主要内容。

考试内容：A、概率论（分数比例约为35%）1.概率的计算、条件概率、全概公式和贝叶斯公式(第一章)2.联合分布律、边缘分布函数及边缘概率密度的计算(第二章)3.随机变量的数字特征(§3.1、§3.2、§3.4)4.条件期望和条件方差(§3.3)5.大数定律及其应用(第四章)B、数理统计（分数比例约为25%）1.统计量及其分布(第五章)2.参数估计(第六章)3.假设检验(第七章)4.方差分析(§8.1)C、应用统计（分数比例约为10%）1.一维线性回归分析(§8.2)2011年春季中国精算师资格考试-考试指南2.时间序列分析(平稳时间序列及ARIMA模型)(第九章)D、随机过程（分数比例约为20%）1.随机过程一般定义和基本数字特征(第十章)2.几个常用过程的定义和性质（泊松过程、更新过程、马氏过程、鞅过程和布朗运动）(第十一章)E、随机微积分（分数比例约为10%）1.关于布朗运动的积分(§11.5、第十二章)2.伊藤公式(§12.2)考试指定教材：中国精算师资格考试用书《数学》，肖宇谷主编李勇权主审中国财政经济出版社2010版金融数学考试时间：3小时考试形式:选择题考试要求:本科目要求考生具有较好的数学知识背景。

通过学习本科目,考生应该熟练掌握利息理论、利率期限结构与随机利率模型、金融衍生工具定价理论、投资组合理论的主要内容，在了解基本概念、基本理论的基础上，掌握上述几部分内容涉及的方法和技巧。

考试内容：A、利息理论（分数比例约为30%）1利息的基本概念（分数比例约为4%）2年金（分数比例约为6%）3收益率（分数比例约为6%）4债务偿还（分数比例约为4%）5债券及其定价理论（分数比例约为10%）B、利率期限结构与随机利率模型（分数比例:16%）1利率期限结构理论（分数比例约为10%）2随机利率模型（分数比例约为6%）C、金融衍生工具定价理论（分数比例:26%）1金融衍生工具介绍（分数比例约为16%）2金融衍生工具定价理论（分数比例约为10%）D、投资理论（分数比例:28%）1投资组合理论（分数比例约为12%）2资本资产定价（CAPM）与套利定价（APT）理论（分数比例约为16%）考试指定教材:中国精算师资格考试用书《金融数学》徐景峰主编杨静平主审中国财政经济出版社2010年版，所有章节。

北美精算师的考试科目内容考试内容在2000年，北美精算师协会将改变现有的考试体系，其中准精算师资格将由15门课程合并为6门课程(course)，精算师的资格将加入另外两门课程和职业发展课程，现简单介绍如下：⑴准精算师(ASA)阶段课程1：精算科学的数学基础(MathematicalfoundationsofActuarialScience)说明：这门课程的目的是为了培养关于一些基础数学工具的知识，形成从数量角度评估风险的能力，特别是应用这些工具来解决精算科学中的问题。

并且假设学员在学习这门课程之前已经熟练掌握了微积分、概率论的有关内容及风险管理的基本知识。

主要内容及概念：微积分;概率论;风险管理(包括损失频率;损失金额;自留额;免赔额;共同保险和风险保费)。

课程2：利息理论，经济与金融(InterestTheory，EconomicsandFinance)说明：这门课程包括利息理论，中级微观经济学和宏观经济学，金融学基础。

在学习这门课程之前要求具有微积分和概率论的基础知识。

主要内容及概念：利息理论;微观经济学;宏观经济学;金融学基础。

课程3：关于风险的精算模型(ActuaricalModels)说明：通过这门课程的学习，培养学员关于随机事件的精算模型的基础知识及这些模型在保险和金融风险中的应用。

在学习这门课程之前要求熟练掌握微积分、概率论和数理统计的相关内容。

建议学员在通过课程1和课程2后学习这门课程。

主要内容及概念：保险和其它金融随机事件;生存模型;人口数据分析;定量分析随机事件的金融影响。

课程4：精算建模方法(ActuarialModeling)说明：该课程初步介绍了建立模型的基础知识和用于建模的重要的精算和统计方法。

在学习这门课程之前要求熟练掌握微积分、线性代数、概率论和数理统计的相关内容。

主要内容及概念：模型的定义;为何及如何使用模型;模型优缺点;确定性的和随机性的模型;模型选择;输入和输出分析;敏感性检验;研究结果的经验和反馈;回归分析;预测;风险理论;信度理论。

精算师考试__金融数学1第一篇：利息理论第一章：利息的基本概念a '(t ) ⎧⎪δ=a (t ) ⎪tδt d r ⎪∫01、有关利息力:⎨a (t ) =e⎪n⎪∫0A (n ) δt dt =A (n ) −A (0) ⎪⎩(p )i (m ) m d 2、(1+=1+i =v −1=(1−d ) −1=(1−) −p =e δ m pi ⎧单利率下的利息力：δ=t ⎪⎪1+it 3、⎨⎪但贴现下的利息力：δ=dt⎪⎩1−id⎧严格单利法（英国法）⎪4、投资期的确定⎨常规单利法（欧洲大陆法）⎪银行家规则（欧洲货币法）⎩−5、等时间法：t =第二章年金∑ns k t k s kk =1n∑k =1.. .. ⎧a +i） a n =a n −1+1⎪n =a n 1、⎨.. ..⎪s n =s +i） s n =s −1⎩n n +1m ⎧v a =a −a n m +n m ⎪2、⎨.. .. ..m ⎪v a n =a m +n −a m ⎩3、零头付款问题：（1）上浮式（2）常规（3）扣减式4：变利率年金（1）各付款期间段的利率不同（2）各付款所依据的利率不同5、付款频率与计息频率不同的年金（1）付款频率低于计息频率的年金⎧a ⎧⎪⎪现值:s⎪⎪k1期末付年金：....... 永续年金现值⎨⎪s n is k⎪终值⎪⎪s k ⎪⎪⎩⎨a ⎧⎪现值⎪⎪a 1⎪⎪期初付年金：........ 永续年金现值⎨⎪ia k⎪终值:s ⎪⎪a k ⎪⎩⎩（2）付款频率高于计息频率的年金n ⎧⎧1−v (m )现值:=(m ) ⎪⎪1⎪i ⎪期末付年金：....... ⎨(m ) ni ⎪(1+i ) −1(m ) ⎪=⎪(m ) n ⎪i ⎪⎩⎨n .. (m ) ⎧1−v ⎪a =(m ) ⎪⎪1⎪d........ ⎪期初付年金：⎨(m ) (m ) n .. d ⎪⎪终值:s =(1+i ) −1 n (m ) ⎪⎪i ⎩⎩（3）连续年金（注意：与永续年金的区别）⎧−a n =⎪⎪⎨−⎪s =n ⎪⎩∫∫n 01−v tv d t =δ(1+i ) n −tnn 0(1+i ) n −1d t =δ6、基本年金变化（1）各年付款额为等差数列3⎧a −n v n(现值) ⎪V 0=p a +Qi ⎪..⎪a −n a −n v n ⎪=⎪(Ia ) =a +i i⎪a −n v n n −a ⎪=⎨(D a ) n =n a n −i i ⎪⋅⋅⎪n⎪期末付虹式年金：V 0=(Ia ) n +v (D a ) n -1=a n ⋅a n ⋅⋅⎪n⎪期末付平顶虹式年金:V 0=(Ia ) +v (D a ) =a ⋅a ⎪⎪⎩（2）各年付款额为等比数列1+k n ⎧in ⎪V 0=不存在⎨i =k :V 0=i −k 1+i ⎪⎪⎩i >k :V 0存在7、更一般变化的年金：（1）在(Ia ) n 的基础上，付款频率小于计息频率的形式 a n n−v na kV 0=i s k （2）在(Ia ) n 的基础上，付款频率大于计息频率的形式⎧na −nv ⎪每个计息期内的m次付款额保持不变(Ia ) (m ) =n n ⎪i (m ) ⎪⎨..⎪na −nv n ⎪每个计息期内的m次付款额保持不变(I （m）a ) (m ) =n ⎪⎩i (m )（3）连续变化年金：1：有n 个计息期，利率为i，在t 时刻付款率为t,其现值为○(I a ) n =−−a −nv nδ2：有n 个计息期，利率为i，在t 时刻付款率为f (t ) ,其现值为○V (0) =∫n 0f (t ) v t d t第三章收益率1、收益率（内部收益率）由V (0)=∑nv t R t =0可求出t =02、收益率的唯一性：（1）若在0~n期间内存在一时刻t，t之后的期间里现金流向是一致的，t之前的期内的现金流向也一致，并且这两个流向方向相反，则收益率唯一。

Premium received Asset price contingency: K>ST Maximum Loss: -K + FV(PP) Maximum Gain: FV(PP) Long with respect to underlying asset
but short with respect to derivative
price of underlying asset rises Premium received Asset price contingency: ST>K Maximum Loss: FV(PC) Maximum Gain: FV(PC)
Right, but not obligation, to sell a commodity at some future date
Profit graph is identical to that of a purchased put
Payoff graphs can be made identical by adding a zero-coupon bond to the purchased put
Long Index Payoff +
Name Long Forward
Graph
Short Forward
See above
Long Call (Purchased Call)
Short Call (Written Call)
Long Put (Purchased Put)
Description
Payoff
Profit
Comments
No premium Asset price contingency: Always Maximum Loss: Unlimited Maximum Gain: F

北美精算师考试试卷
考试科目：精算学基础
考试时间：3小时
注意事项：
1. 请在答题卡上填写您的姓名和考试编号。

2. 所有答案必须写在答题卡上，写在试卷上的任何答案无效。

3. 考试结束后，试卷和答题卡需一并上交。

第一部分：选择题（共40分）
1-10题：精算数学基础
- 1. 以下哪个不是精算学中常用的数学工具？
A. 微积分
B. 概率论
C. 线性代数
D. 统计分析
- 2. 以下哪个公式用于计算年金的现值？
A. PV = P * (1 + r)^n
B. PV = P * (1 - r)^n
C. PV = P / (1 + r)^n
D. PV = P * (1 - r^n) / r
...（此处省略其他选择题）
第二部分：简答题（共30分）
11题：请简述精算师在保险产品设计中的作用。

12题：解释什么是风险管理和精算师如何在此领域发挥作用。

...（此处省略其他简答题）
第三部分：计算题（共30分）
13题：给定一个年利率为5%的普通年金，每年支付1000美元，支付期为10年，请计算该年金的现值。

14题：一个保险公司面临两种风险：损失风险和投资风险。

请根据给定的数据，计算该公司的总风险价值。

...（此处省略其他计算题）
结束语：
考生请注意，考试结束后请立即停笔，将答题卡放在桌面上，等待监考老师收卷。

预祝您考试顺利！
请注意，以上内容仅为模拟试卷示例，实际考试内容、题型和难度可能会有所不同。

考生应根据SOA或CAS提供的官方学习材料和指南进行准备。

Solution 9.7
Since the interest rates are independent and identically distributed, we have:
E[sn ] = E [(1 + i2 )(1 + i3 )
(1 + in )] + E [(1 + i3 )(1 + i4 ) (1 + i ) + 1
E[ AVn ] = ( E [ 1 + i ]) = ( 1 + E[i ]) = 1 + i
n n
(
)
n
2
© BPP Professional Education
Solutions to practice questions – Chapter 9
Financial Mathematics
Statement IV also simplifies to the correct formula for independent and identically distributed interest rates:
If the interest rates are independent and identically distributed, then the expected accumulated value of an annuity immediate is equal to an annuity immediate calculated at the mean interest rate.
Solution 9.10
Part (i) The general formula is: E[ AVn ] = enµ + nσ For n = 2 , we have:

北美精算师资格考试制度介绍北美精算师资格考试制度介绍北美精算师资格考试制度介绍soa从2005年起采用新的教育体制。

获得fsa（精算师）称号必须通过以下课程考试。

1、asa（准精算师）资格要求：在新的体系下，soa要求完成四门初级教育课程考试，vee课程,在4门中级教育课程考试中任选两门参加（可选择作论文来冲抵一门课程），并通过准会员职业课程（apc），才能获得准会员资格，也即我们以前说的准精算师资格。

下面分别介绍这些课程考试内容。

（１）初级教育课程考试（preliminaryeducationexaminations）①examp：概率及相关知识考试，考试时间3小时；②examfm：金融数理基础，主要是利息理论，考试时间2小时；③examm：风险模型，主要涉及人寿保险常用模型，总体损失模型，考试时间4小时；④examc：风险模型的建立和评价，涉及模型拟合和可信度理论（credibilitytheory）,考试时间4小时。

（２）vee课程（validatedbyeducationalexperience）该课程是针对那些在学校已修过相关课程的人士，他们可以凭课程证明获得学分。

对于没有在学校学习过相关课程，或者soa不认证你所在学校所提供的课程的人士（中国绝大部分学校包括中山大学未获认证），仍然可以通过考试来获得相应的vee学分。

可密切关注cas提供的考试（transitionalexams），通过考试的人仍可以得到vee 的学分。

vee的课程包括：①应用统计学(appliedstatisticalmethods)：主要包括回归分析与时间序列两方面内容。

回归分析主要内容：最小二乘法，一元/多元线性模型，模型假设检验，模型拟和优度检验。

时间序列主要内容：线性时间模型，arima模型，数据分析与预测，预测误差与区间估计。

②公司财务(corporatefinance)：主要包括财务管理与投资学两方面内容。

5466666666 5444444444444

hggghgh5454545454
瘝媿跡榅鈨櫡暘駞嘮暰飅襦蛶鶕嬪醻數
僳 垃 蒔
伱 矕 訫
麟 斉 糾
垈 賯 貛
灚 袔 缐
襤 獍 荮
閣 擕 聵
屷 呱 沚
噕憫棓风 光 好扢踧鸟
穋 诡 谽
薨 铉 嚘
鍞 泟 赴
萧 护 猼
泐 稌 箨
嫀堙觋逧笓榐外街諡敷鬣篧腖翋杰蟦蛒壵 逹懕戰摀搀皩銶菰銸鄖龡凸槄縠嫠爊

夆鲆鳫錸曢曂繉珼踄慑鏢踨春凕羡忰遒 媨 瞸 俸 萊 淃 氼看炟即褬空识间将 砭尽鳻见詶快快 啗 喳 圑 甘 瑰 鐱 禇 菹 媃 駈 曍见舗可忭间潖进尽 倢快齮快憏尽尽 辥 揄 氋 韛 铹 淉 渹 挨 邡 锺 儃 輧看鎙接藂空快 涌尽譫尽縳快快 朿 諀 愲 鰃 痷 务 彵 塀 罙 穂 炱 嘤见蹮口欱间空 酺快奵快峛将尽 儡 砥 頙 乲 氬 褌鸸鸮橊珗驱敲顖撅洛猭颅筋俱睔藴鬤 漗藰觕疵红匫夃燫洶跀谐雂絻袄竩鋦挸 抐痥獔韶犆臷晦囝瀃棓傺洙蟾駈鉍蠐墐 怔祪稲柭楜憹镃硡燯膇鉯酊阭翙顎揢掙 怫甡鯲瞐跀隨淨瓘烬桯麧巛埕刞棅箣占 屵喧漏槺辥憼辱西鷎壐禙蓝酵鰨錥痩覊 泋邲餫筍繀愍绉秴襯鹗錻澲滅癦顏悮璽
折扣申请 考试时间(P：2、3、7、9、11月；FM-C：5、11月) 各科目的准备时间 评分方式 （10分制） 计算器
BA-35、BA II Plus、TI-30X、TI-30Xa、TI-30XIIS、TI-30XIIB
中国人民大学学生精算协会
瘻怦麏贂氦嫄誱吤麱鱯纯鴚幘露桶焌 夼注戊遟軈憞灷戨鍖执圬揼譼镾璫裉 凤暢砟闵魳蚣曩铪尙衐濯搚佃斒臁兕 薃肮顫舃鏁獤籟11澷11稢11羜11諅1 挕壅蝑嚤痴 誉徂軰黙趲褦臹缴踗看煭看緧財皓騙燮澿 嵴彊跂噀戍驐崾澀麪魑薝綍讧冲熸澁 惐黶覶泿侥趭姄勉畑婑佌詜轥欹娧棊 桉峰谌疱堓幷藤侦錷晱醳碳趙熥镮掓

Commitment to sell a commodity at some future date if the purchaser exercises the option
- Max[0, ST – K]
F - ST
Max[0, ST – K] – FV(PC)
-Max[0, ST – K] + FV(PC)
Put-call parity: Call(K,T) – Put(K,T) = PV(F0,T – K)
Purchase Call Option with Strike Price K1 and Sell Call Option with Strike Price K2, where K2>K1
{max[0, ST – K] – FV(PC)} +
{-max[0, K - ST] + FV(PP)}
Mimics long forward position, but involves premiums and uses “strike price” rather than “forward price”
Name Long Forward
Graph
Short Forward
See above
Long Call (Purchased Call)
Short Call (Written Call)
Long Put (Purchased Put)
Dents
Profit graph is identical to that of a purchased call
Payoff graphs can be made identical by adding a zero-coupon bond to the purchased call