話說看電影吃東西這件事情,
就想到我開始看電影的故事,
如同你我所知,電影院裡面的附餐真的是貴到"逼~"(消音)
所以窮學生的我,只好都用偷渡的.
工具有很多,大衣,包包,孕婦裝等等
當然吃的時候也要顧及旁邊人的感受,味道太重的東西實在不適合在電影院
這種密閉空間吃,就好像在辦公室吃臭豆腐或是麻辣鴨血還是榴璉都是不道德低。
雖然現在都用信用卡看,兩個人會送兩杯小飲料和個爆米花只要260,
但偶爾看到狀似學生且做以前做過的動作時也會勾起回憶!
是老了嗎?都開始往回看了.....
對了,linkin park的演唱會你有要去嗎@@?
我剛好撞期不能過去......
不過怎麼好像也不多人知道的樣子
聽著what I've done真的會讓我想著這數十年...what I've done...
這算是...老頭碎碎唸嗎?
Wednesday, April 1, 2009
回憶
希望你真的可以趕快找到一個人的空間
我家只有三個人
老媽 我 老妹
所以老媽希望我們三個人可以常常團圓
甚至住在一起
但...我在台北工作
老妹在台中唸書...之後應該會去美國
老媽在彰化工作
壓跟就是分離四散東西,也無法改變什麼
之前也試過大家聚在一起,不過視自由為性命的我跟老妹(超不孝的)
沒幾天就受不了了.....
我家只有三個人
老媽 我 老妹
所以老媽希望我們三個人可以常常團圓
甚至住在一起
但...我在台北工作
老妹在台中唸書...之後應該會去美國
老媽在彰化工作
壓跟就是分離四散東西,也無法改變什麼
之前也試過大家聚在一起,不過視自由為性命的我跟老妹(超不孝的)
沒幾天就受不了了.....
Monday, March 23, 2009
影fu~花吃了那女孩(Candy rain)
由四段故事集合而成,每段各自代表愛情的某些成面。
就如同陳綺貞旁白描述著的
如果南國冰封了代表在一起很快樂,
看不見攻擊的城市代表不在一起比較快樂,
夢見相反的夢代表不在一起不快樂,
像花吃了那女孩代表即使在一起也不快樂.
影像的呈現和音樂的使用都相當舒適,幾首裡面量身訂做的歌曲更是好聽.
裡面令我感受最深刻的故事應該是.."夢見相反的夢"
由高伊玲飾演的summer,對著波麗士大人的檢察官(spancer)說
我只不過是去完成個義務罷了,等我完成社會的期許(結婚和生孩子),
我就回來了~
很欣賞這個角色的率性,與對自我認知的了解,雖然我已逼近30關頭,對於所要所需
卻還是常常迷惘,很難很堅定的說出這些話,尤其是帶著一片輕鬆的表情.
女女的戀情總是讓我有種很美的感覺,不管是現實上或者在電影上面所遇見的，
但不知為什麼,對於男男卻無法放開心胸來接受(朋友是可以啦,電影就看不太下去),
想著想著
香格里拉的歌詞就浮現腦海
【香格里拉】
作詞：黃玠 作曲：黃玠
我以為認真去做就能實現我的夢
以為寫首好歌走路就能抬起頭
以為騎摩托車旅行就能變英雄
現在的我失去了衝動
有才華的人唾棄金光閃閃的獎座
親愛的 Cobain 是否也曾愛慕虛榮
多希望有人衝破疑惑帶我向前走
現在的我變的好懦弱
雨會下雨會停 這是不變的道理
夜空中北極星 迷路的人不恐懼
我唱歌你在聽 一切風平又浪靜
Ｇ和絃的根音 撫平脆弱的心靈
我只想牽著你 走到很遠的夢裡
小木屋紅屋頂 地址是一個秘密
你抱著小貓咪 藍眼睛不再憂鬱
就如同陳綺貞旁白描述著的
如果南國冰封了代表在一起很快樂,
看不見攻擊的城市代表不在一起比較快樂,
夢見相反的夢代表不在一起不快樂,
像花吃了那女孩代表即使在一起也不快樂.
影像的呈現和音樂的使用都相當舒適,幾首裡面量身訂做的歌曲更是好聽.
裡面令我感受最深刻的故事應該是.."夢見相反的夢"
由高伊玲飾演的summer,對著波麗士大人的檢察官(spancer)說
我只不過是去完成個義務罷了,等我完成社會的期許(結婚和生孩子),
我就回來了~
很欣賞這個角色的率性,與對自我認知的了解,雖然我已逼近30關頭,對於所要所需
卻還是常常迷惘,很難很堅定的說出這些話,尤其是帶著一片輕鬆的表情.
女女的戀情總是讓我有種很美的感覺,不管是現實上或者在電影上面所遇見的，
但不知為什麼,對於男男卻無法放開心胸來接受(朋友是可以啦,電影就看不太下去),
想著想著
香格里拉的歌詞就浮現腦海
【香格里拉】
作詞：黃玠 作曲：黃玠
我以為認真去做就能實現我的夢
以為寫首好歌走路就能抬起頭
以為騎摩托車旅行就能變英雄
現在的我失去了衝動
有才華的人唾棄金光閃閃的獎座
親愛的 Cobain 是否也曾愛慕虛榮
多希望有人衝破疑惑帶我向前走
現在的我變的好懦弱
雨會下雨會停 這是不變的道理
夜空中北極星 迷路的人不恐懼
我唱歌你在聽 一切風平又浪靜
Ｇ和絃的根音 撫平脆弱的心靈
我只想牽著你 走到很遠的夢裡
小木屋紅屋頂 地址是一個秘密
你抱著小貓咪 藍眼睛不再憂鬱
Saturday, March 21, 2009
寂寞咬上了我
寂寞咬上了我....
一個人的Brezze,一個人的紀伊國屋,旁邊一對一隊的人們.
讓我感受自己好像裸體在這個空間.
好寂寞,好lonely....
是窘迫嗎?還是有點羞恥?怎麼自己一個人逛街好像變得十惡不赦?
酸酸的感覺泛在心頭,是難過著那個人?還是只是不甘寂寞?
眼光游移,想找著跟我一樣的人,希望找尋著跟我有相同氣味的人.
同樣氣味的人會有類似的行為,眼神期盼著些什麼,真正接觸時卻
跑到其他的地方.是不確定?害怕?甚或是...一點點驕傲?
到了超市拿了罐蜂蜜綠茶,清香甜彌補了內心的微酸.
正當舒緩的瞬間,藉著鋼門的反射....我看到了,
寂寞咬上了我......
一個人的Brezze,一個人的紀伊國屋,旁邊一對一隊的人們.
讓我感受自己好像裸體在這個空間.
好寂寞,好lonely....
是窘迫嗎?還是有點羞恥?怎麼自己一個人逛街好像變得十惡不赦?
酸酸的感覺泛在心頭,是難過著那個人?還是只是不甘寂寞?
眼光游移,想找著跟我一樣的人,希望找尋著跟我有相同氣味的人.
同樣氣味的人會有類似的行為,眼神期盼著些什麼,真正接觸時卻
跑到其他的地方.是不確定?害怕?甚或是...一點點驕傲?
到了超市拿了罐蜂蜜綠茶,清香甜彌補了內心的微酸.
正當舒緩的瞬間,藉著鋼門的反射....我看到了,
寂寞咬上了我......
Monday, March 16, 2009
the info of MFE
LEARNING OUTCOMES – FINANCIAL ECONOMICS SEGMENT
A. Interest rate models
1. Evaluate features of the Vasicek and Cox-Ingersoll-Ross bond price models.
2. Explain why the time-zero yield curve in the Vasicek and Cox-Ingersoll-Ross bond price models cannot be exogenously prescribed.
3. Construct a Black-Derman-Toy binomial model matching a given time-zero yield curve and a set of volatilities.
B. Rational valuation of derivative securities
1. Use put-call parity to determine the relationship between prices of European put and call options and to identify arbitrage opportunities.
2. Calculate the value of European and American options using the binomial model.
3. Calculate the value of European and American options using the Black-Scholes option-pricing model.
4. Interpret the option Greeks.
5. Explain the cash flow characteristics of the following exotic options: Asian, barrier, compound, gap, and exchange.
6. Explain what it means to say that stock prices follow a diffusion process.
7. Apply Itô’s lemma in the one-dimensional case.
8. Apply option pricing concepts to actuarial problems such as equity-linked insurance.
C. Risk management techniques
1. Explain and demonstrate how to control risk using the method of delta-hedging.
Note: Concepts, principles and techniques needed for Exam MFE are covered in the reference 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. The # indicates new or updated material or changes in the sections selected.
Texts – Financial Economics Segment *
• # Derivatives Markets (Second Edition), 2006, by McDonald, R.L.,
Chapter 9,
Chapter 10, (excluding “Options on Commodities” on page 334),
Chapter 11, Sections 11.1 – 11.4, Appendices 11.A and 11.B,
Chapter 12, Sections 12.1–12.5, Appendix 12.A,
Chapter 13, including Appendix 13.B,
Chapter 14,
Chapter 20, Sections 20.1–20.6 (up to but excluding “Multivariate Itô’s Lemma” on pages 665-666) and 20.7 (up to but excluding “Valuing a Claim on SaQb on pages 670-672 and excluding “Finding the lease rate” on top one-half of page 669),
Chapter 21, Sections 21.1 – 21.2 (excluding “What If the Underlying Asset Is Not and Investment Asset” on pages 688-690) and 21.3 (excluding “The Backward Equation” on pages 691-692, and excluding the paragraph on page 692 that begins “If a probability…” and through the end of the section),
Chapter 22, Section 22.1 (but with only those definitions in Tables 22.1 and 22.2 that are relevant to Section 22.1),
Chapter 23, Sections 23.1 – 23.2 (up to but excluding “Exponentially Weighted Moving Average” on page 746 and through the end of the section),
Chapter 24, Sections 24.1–24.5 (up to but excluding “Forward rate agreements” on pages 806-808),
Appendix B.1, Appendix C, and including relevant Errata (see below).
Unless otherwise stated chapter appendices are not included in the required readings from this text.
*Any textbook errata are included below.
Study Notes - Financial Economics Segment
Title
Exam MFE/Exam 3F Tables
Some Remarks on Derivatives Markets
Derivatives Markets, Errata 2006 Second Edition, by R. McDonald,
http://www.kellogg.northwestern.edu/faculty/mcdonald/htm/typos2e.html
All released exam papers, since 2000 can be found here.
Exam MFE/3F Sample Questions and Solutions (1–49) - 02.23.09
A. Interest rate models
1. Evaluate features of the Vasicek and Cox-Ingersoll-Ross bond price models.
2. Explain why the time-zero yield curve in the Vasicek and Cox-Ingersoll-Ross bond price models cannot be exogenously prescribed.
3. Construct a Black-Derman-Toy binomial model matching a given time-zero yield curve and a set of volatilities.
B. Rational valuation of derivative securities
1. Use put-call parity to determine the relationship between prices of European put and call options and to identify arbitrage opportunities.
2. Calculate the value of European and American options using the binomial model.
3. Calculate the value of European and American options using the Black-Scholes option-pricing model.
4. Interpret the option Greeks.
5. Explain the cash flow characteristics of the following exotic options: Asian, barrier, compound, gap, and exchange.
6. Explain what it means to say that stock prices follow a diffusion process.
7. Apply Itô’s lemma in the one-dimensional case.
8. Apply option pricing concepts to actuarial problems such as equity-linked insurance.
C. Risk management techniques
1. Explain and demonstrate how to control risk using the method of delta-hedging.
Note: Concepts, principles and techniques needed for Exam MFE are covered in the reference 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. The # indicates new or updated material or changes in the sections selected.
Texts – Financial Economics Segment *
• # Derivatives Markets (Second Edition), 2006, by McDonald, R.L.,
Chapter 9,
Chapter 10, (excluding “Options on Commodities” on page 334),
Chapter 11, Sections 11.1 – 11.4, Appendices 11.A and 11.B,
Chapter 12, Sections 12.1–12.5, Appendix 12.A,
Chapter 13, including Appendix 13.B,
Chapter 14,
Chapter 20, Sections 20.1–20.6 (up to but excluding “Multivariate Itô’s Lemma” on pages 665-666) and 20.7 (up to but excluding “Valuing a Claim on SaQb on pages 670-672 and excluding “Finding the lease rate” on top one-half of page 669),
Chapter 21, Sections 21.1 – 21.2 (excluding “What If the Underlying Asset Is Not and Investment Asset” on pages 688-690) and 21.3 (excluding “The Backward Equation” on pages 691-692, and excluding the paragraph on page 692 that begins “If a probability…” and through the end of the section),
Chapter 22, Section 22.1 (but with only those definitions in Tables 22.1 and 22.2 that are relevant to Section 22.1),
Chapter 23, Sections 23.1 – 23.2 (up to but excluding “Exponentially Weighted Moving Average” on page 746 and through the end of the section),
Chapter 24, Sections 24.1–24.5 (up to but excluding “Forward rate agreements” on pages 806-808),
Appendix B.1, Appendix C, and including relevant Errata (see below).
Unless otherwise stated chapter appendices are not included in the required readings from this text.
*Any textbook errata are included below.
Study Notes - Financial Economics Segment
Title
Exam MFE/Exam 3F Tables
Some Remarks on Derivatives Markets
Derivatives Markets, Errata 2006 Second Edition, by R. McDonald,
http://www.kellogg.northwestern.edu/faculty/mcdonald/htm/typos2e.html
All released exam papers, since 2000 can be found here.
Exam MFE/3F Sample Questions and Solutions (1–49) - 02.23.09
the info of C
Exam C Construction and Evaluation of Actuarial Models
Exam C is a four-hour multiple choice examination and is identical to CAS Exam 4. The examination is jointly sponsored and administered by the SOA, CAS, and the Canadian Institute of Actuaries (CIA). The examination is also jointly sponsored by the American Academy of Actuaries (AAA) and the Conference of Consulting Actuaries (CCA). The syllabus for this examination provides an introduction to modeling and covers important actuarial methods that are useful in modeling. A thorough knowledge of calculus and probabilityis assumed.
The candidate will be introduced to useful frequency and severity models beyond those covered in Exam M. The candidate will be required to understand the steps involved in the modeling process and how to carry out these steps in solving business problems. The candidate should be able to: 1) analyze data from an application in a business context; 2) determine a suitable model including parameter values; and 3) provide measures of confidence for decisions based upon the model. The candidate will be introduced to a variety of tools for the calibration and evaluation of the models.
A variety of tables is available for the candidate on the SOA Web site and will be provided to the candidate at the examination. These include values for the standard normal distribution, chi-square distribution, and abridged inventories of discrete and continuous probability distributions. Since they will be provided at the examination, candidates will not be allowed to bring copies of the tables into the examination room. Check the Updates section of the SOA Web site for any changes to the exam or syllabus.
LEARNING OUTCOMES
The candidate is expected to be familiar with survival, severity, frequency and aggregate models, and use statistical methods to estimate parameters of such models given sample data. The candidate is further expected to identify steps in the modeling process, understand the underlying assumptions implicit in each family of models, recognize which assumptions are applicable in a given business application, and appropriately adjust the models for impact of insurance coverage modifications.
Specifically, the candidate is expected to be able to perform the tasks listed below:
LEARNING OUTCOMES
A. Severity Models
1. Calculate the basic distributional quantities:
a) Moments
b) Percentiles
c) Generating functions
2. Describe how changes in parameters affect the distribution.
3. Recognize classes of distributions and their relationships.
4. Apply the following techniques for creating new families of distributions:
a) Multiplication by a constant
b) Raising to a power
c) Exponentiation,
d) Mixing
5. Identify the applications in which each distribution is used and reasons why.
6. Apply the distribution to an application, given the parameters.
Exam C Construction and Evaluation of Actuarial Models
Spring 2009
7. Calculate various measures of tail weight and interpret the results to compare the tail weights.
8. Explain the properties of the lognormal distribution.
9. Explain the Black-Scholes formula as a limited expected value for a lognormal distribution.
B. Frequency Models
For the Poisson, Mixed Poisson, Binomial, Negative Binomial, Geometric distribution and mixtures thereof (as well as compound distributions):
1. Describe how changes in parameters affect the distribution,
2. Calculate moments,
3. Identify the applications for which each distribution is used and reasons why,
4. Apply the distribution to an application given the parameters.
C. Aggregate Models
1. Compute relevant parameters and statistics for collective risk models.
2. Evaluate compound models for aggregate claims.
3. Compute aggregate claims distributions.
D. For severity, frequency and aggregate models,
1. Evaluate the impacts of coverage modifications:
a) Deductibles
b) Limits
c) Coinsurance
2. Calculate Loss Elimination Ratios.
3. Evaluate effects of inflation on losses.
E. Risk Measures
1. Calculate VaR, CTE, and other risk measures and explain their use and limitations
F. Ruin Theory
1. Calculate survival and ruin probabilities using discrete models.
2. Describe the considerations included in a ruin model
G. Construction of Empirical Models
1. Estimate failure time and loss distributions using:
a) Kaplan-Meier estimator, including approximations for large data sets
b) Nelson-Åalen estimator
c) Kernel density estimators
2. Estimate the variance of estimators and confidence intervals for failure time and loss distributions.
3. Estimate failure time and loss distributions with the Cox proportional hazards model and other basic models with covariates.
4. Apply the following concepts in estimating failure time and loss distribution:
a) Unbiasedness
b) Consistency
c) Mean squared error
H. Construction and Selection of Parametric Models
1. Estimate the parameters of failure time and loss distributions using:
a) Maximum likelihood
b) Method of moments
c) Percentile matching
d) Bayesian procedures
2. Estimate the parameters of failure time and loss distributions with censored and/or truncated data using maximum likelihood.
3. Estimate the variance of estimators and the confidence intervals for the parameters and functions of parameters of failure time and loss distributions.
4. Apply the following concepts in estimating failure time and loss distributions:
a) Unbiasedness
b) Asymptotic unbiasedness
c) Consistency
d) Mean squared error
e) Uniform minimum variance
5. Determine the acceptability of a fitted model and/or compare models using:
a) Graphical procedures
b) Kolmogorov-Smirnov test
c) Anderson-Darling test
d) Chi-square goodness-of-fit test
e) Likelihood ratio test
I. Credibility
1. Apply limited fluctuation (classical) credibility including criteria for both full and partial credibility.
2. Perform Bayesian analysis using both discrete and continuous models.
3. Apply Bühlmann and Bühlmann-Straub models and understand the relationship of these to the Bayesian model.
4. Apply conjugate priors in Bayesian analysis and in particular the Poisson-gamma model.
5. Apply empirical Bayesian methods in the nonparametric and semiparametric cases.
J. Simulation
1. Simulate both discrete and continuous random variables using the inversion method.
2. Estimate the number of simulations needed to obtain an estimate with a given error and a given degree of confidence.
3. Use simulation to determine the p-value for a hypothesis test.
4. Use the bootstrap method to estimate the mean squared error of an estimator.
5. Apply simulation methods within the context of actuarial models.
6. Simulate lognormal stock prices.
7. Incorporate jumps in stock prices by mixing Poisson and lognormal random variables.
8. Use variance reduction techniques to accelerate convergence.
9. Use the Cholesky decomposition method for simulating correlated random variables.
Texts*
• Loss Models: From Data to Decisions, (Third Edition), 2008, by Klugman, S.A., Panjer, H.H. and Willmot, G.E., Chapter 3, Sections 3.1– 3.4 (excluding example 3.6), Chapter 4, Chapter 5, Sections 5.1– 5.4, Chapter 6, Sections 6.1– 6.5 and 6.7, Chapter 8, Chapter 9, Sections 9.1–9.7 (excluding 9.6.1 and examples 9.9 and 9.11), Sections
9.11.1–9.11.2, Chapter 10, Sections 10.1, 10.2.3 and 10.3, Chapters 12–14, Chapter 15, Sections 15.1–15.3, 15.5, 15.6.1–15.6.3,15.6.6, Chapter 16, Chapter 17, Section 17.3, Chapter 21, Sections 21.1–21.2.3, and 21.2.6 Note: Candidates may also use the Second Edition of Loss Models, (2004). The following chapter references apply: Chapter 3, Chapter 4, Sections 4.1-4.6.6, Chapter 5, Chapter 6, Sections 6.1–6.7 (excluding 6.6.1), 6.11.1, Chapter 7, Sections 7.1, 7.2.3, 7.3.1, 7.3.2, Chapters 9–11, Chapter 12 (excluding 12.5.4, 12.5.5 and 12.6), Chapter 13 Chapter 17.
• Derivatives Markets (Second Edition), 2006, by McDonald, R.L., Chapters 18-19, excluding appendices. [Including Errata]
Reading Options for Credibility
The candidate may use any of the alternatives shown below.
Option A
• Loss Models: From Data to Decisions, (Third Edition), 2008, by Klugman, S.A., Panjer, H.H., and Willmot, G.E., , Chapter 20, Sections 20.2, 20.3 (excluding 20.3.8), 20.4 (excluding 20.4.3)
Note: For Candidates using the Second Edition of Loss Models, the chapter references are:
Chapter 16, Sections 16.1–16.2 (background only), Sections 16.3, 16.4 (excluding 16.4.7), 16.5 (excluding 16.5.3). [Including Errata]
Option B
• Foundations of Casualty Actuarial Science (Fourth Edition), 2001, Casualty Actuarial Society, , “Credibility”, by Mahler, H.C., and Dean C.G., Chapter 8, Section 1 (background only) Sections 2–5 (Available as Study Note C-21-01).
• Topics in Credibility Theory (Study Note C-24-05) by Dean, C.G.
Option C
• Introduction to Credibility Theory (Third Edition), 1999, Herzog, T.N., Chapter 1-3 (background only) Chapters 4–8
Chapter 9 (background only)
*Any textbook errata are included below.
Study Notes: The # indicates new or updated material.
Code Title
Tables for Exam C/Exam 4 - Update 01.12.09
Loss Models Errata Second Edition http://www.soa.org/files/pdf/lm2e-errata%20070606.pdf Derivatives Markets, Errata, 2006 Second Edition, by R. McDonald
http://www.kellogg.northwestern.edu/faculty/mcdonald/htm/typos2e.html
Past Exams All released exam papers since 2000, can be found at:
http://www.soa.org/education/exam-req/syllabus-study-materials/edu-multiple-choice-exam.aspx
C-09-08 Exam C Sample Questions and Solutions
C-21-01 Credibility (to be used with Option B only)
C-24-05 Topics in Credibility Theory (to be used with Option B only)
C-25-07 An Introduction to Risk Measures for Actuarial Applications
Exam C is a four-hour multiple choice examination and is identical to CAS Exam 4. The examination is jointly sponsored and administered by the SOA, CAS, and the Canadian Institute of Actuaries (CIA). The examination is also jointly sponsored by the American Academy of Actuaries (AAA) and the Conference of Consulting Actuaries (CCA). The syllabus for this examination provides an introduction to modeling and covers important actuarial methods that are useful in modeling. A thorough knowledge of calculus and probabilityis assumed.
The candidate will be introduced to useful frequency and severity models beyond those covered in Exam M. The candidate will be required to understand the steps involved in the modeling process and how to carry out these steps in solving business problems. The candidate should be able to: 1) analyze data from an application in a business context; 2) determine a suitable model including parameter values; and 3) provide measures of confidence for decisions based upon the model. The candidate will be introduced to a variety of tools for the calibration and evaluation of the models.
A variety of tables is available for the candidate on the SOA Web site and will be provided to the candidate at the examination. These include values for the standard normal distribution, chi-square distribution, and abridged inventories of discrete and continuous probability distributions. Since they will be provided at the examination, candidates will not be allowed to bring copies of the tables into the examination room. Check the Updates section of the SOA Web site for any changes to the exam or syllabus.
LEARNING OUTCOMES
The candidate is expected to be familiar with survival, severity, frequency and aggregate models, and use statistical methods to estimate parameters of such models given sample data. The candidate is further expected to identify steps in the modeling process, understand the underlying assumptions implicit in each family of models, recognize which assumptions are applicable in a given business application, and appropriately adjust the models for impact of insurance coverage modifications.
Specifically, the candidate is expected to be able to perform the tasks listed below:
LEARNING OUTCOMES
A. Severity Models
1. Calculate the basic distributional quantities:
a) Moments
b) Percentiles
c) Generating functions
2. Describe how changes in parameters affect the distribution.
3. Recognize classes of distributions and their relationships.
4. Apply the following techniques for creating new families of distributions:
a) Multiplication by a constant
b) Raising to a power
c) Exponentiation,
d) Mixing
5. Identify the applications in which each distribution is used and reasons why.
6. Apply the distribution to an application, given the parameters.
Exam C Construction and Evaluation of Actuarial Models
Spring 2009
7. Calculate various measures of tail weight and interpret the results to compare the tail weights.
8. Explain the properties of the lognormal distribution.
9. Explain the Black-Scholes formula as a limited expected value for a lognormal distribution.
B. Frequency Models
For the Poisson, Mixed Poisson, Binomial, Negative Binomial, Geometric distribution and mixtures thereof (as well as compound distributions):
1. Describe how changes in parameters affect the distribution,
2. Calculate moments,
3. Identify the applications for which each distribution is used and reasons why,
4. Apply the distribution to an application given the parameters.
C. Aggregate Models
1. Compute relevant parameters and statistics for collective risk models.
2. Evaluate compound models for aggregate claims.
3. Compute aggregate claims distributions.
D. For severity, frequency and aggregate models,
1. Evaluate the impacts of coverage modifications:
a) Deductibles
b) Limits
c) Coinsurance
2. Calculate Loss Elimination Ratios.
3. Evaluate effects of inflation on losses.
E. Risk Measures
1. Calculate VaR, CTE, and other risk measures and explain their use and limitations
F. Ruin Theory
1. Calculate survival and ruin probabilities using discrete models.
2. Describe the considerations included in a ruin model
G. Construction of Empirical Models
1. Estimate failure time and loss distributions using:
a) Kaplan-Meier estimator, including approximations for large data sets
b) Nelson-Åalen estimator
c) Kernel density estimators
2. Estimate the variance of estimators and confidence intervals for failure time and loss distributions.
3. Estimate failure time and loss distributions with the Cox proportional hazards model and other basic models with covariates.
4. Apply the following concepts in estimating failure time and loss distribution:
a) Unbiasedness
b) Consistency
c) Mean squared error
H. Construction and Selection of Parametric Models
1. Estimate the parameters of failure time and loss distributions using:
a) Maximum likelihood
b) Method of moments
c) Percentile matching
d) Bayesian procedures
2. Estimate the parameters of failure time and loss distributions with censored and/or truncated data using maximum likelihood.
3. Estimate the variance of estimators and the confidence intervals for the parameters and functions of parameters of failure time and loss distributions.
4. Apply the following concepts in estimating failure time and loss distributions:
a) Unbiasedness
b) Asymptotic unbiasedness
c) Consistency
d) Mean squared error
e) Uniform minimum variance
5. Determine the acceptability of a fitted model and/or compare models using:
a) Graphical procedures
b) Kolmogorov-Smirnov test
c) Anderson-Darling test
d) Chi-square goodness-of-fit test
e) Likelihood ratio test
I. Credibility
1. Apply limited fluctuation (classical) credibility including criteria for both full and partial credibility.
2. Perform Bayesian analysis using both discrete and continuous models.
3. Apply Bühlmann and Bühlmann-Straub models and understand the relationship of these to the Bayesian model.
4. Apply conjugate priors in Bayesian analysis and in particular the Poisson-gamma model.
5. Apply empirical Bayesian methods in the nonparametric and semiparametric cases.
J. Simulation
1. Simulate both discrete and continuous random variables using the inversion method.
2. Estimate the number of simulations needed to obtain an estimate with a given error and a given degree of confidence.
3. Use simulation to determine the p-value for a hypothesis test.
4. Use the bootstrap method to estimate the mean squared error of an estimator.
5. Apply simulation methods within the context of actuarial models.
6. Simulate lognormal stock prices.
7. Incorporate jumps in stock prices by mixing Poisson and lognormal random variables.
8. Use variance reduction techniques to accelerate convergence.
9. Use the Cholesky decomposition method for simulating correlated random variables.
Texts*
• Loss Models: From Data to Decisions, (Third Edition), 2008, by Klugman, S.A., Panjer, H.H. and Willmot, G.E., Chapter 3, Sections 3.1– 3.4 (excluding example 3.6), Chapter 4, Chapter 5, Sections 5.1– 5.4, Chapter 6, Sections 6.1– 6.5 and 6.7, Chapter 8, Chapter 9, Sections 9.1–9.7 (excluding 9.6.1 and examples 9.9 and 9.11), Sections
9.11.1–9.11.2, Chapter 10, Sections 10.1, 10.2.3 and 10.3, Chapters 12–14, Chapter 15, Sections 15.1–15.3, 15.5, 15.6.1–15.6.3,15.6.6, Chapter 16, Chapter 17, Section 17.3, Chapter 21, Sections 21.1–21.2.3, and 21.2.6 Note: Candidates may also use the Second Edition of Loss Models, (2004). The following chapter references apply: Chapter 3, Chapter 4, Sections 4.1-4.6.6, Chapter 5, Chapter 6, Sections 6.1–6.7 (excluding 6.6.1), 6.11.1, Chapter 7, Sections 7.1, 7.2.3, 7.3.1, 7.3.2, Chapters 9–11, Chapter 12 (excluding 12.5.4, 12.5.5 and 12.6), Chapter 13 Chapter 17.
• Derivatives Markets (Second Edition), 2006, by McDonald, R.L., Chapters 18-19, excluding appendices. [Including Errata]
Reading Options for Credibility
The candidate may use any of the alternatives shown below.
Option A
• Loss Models: From Data to Decisions, (Third Edition), 2008, by Klugman, S.A., Panjer, H.H., and Willmot, G.E., , Chapter 20, Sections 20.2, 20.3 (excluding 20.3.8), 20.4 (excluding 20.4.3)
Note: For Candidates using the Second Edition of Loss Models, the chapter references are:
Chapter 16, Sections 16.1–16.2 (background only), Sections 16.3, 16.4 (excluding 16.4.7), 16.5 (excluding 16.5.3). [Including Errata]
Option B
• Foundations of Casualty Actuarial Science (Fourth Edition), 2001, Casualty Actuarial Society, , “Credibility”, by Mahler, H.C., and Dean C.G., Chapter 8, Section 1 (background only) Sections 2–5 (Available as Study Note C-21-01).
• Topics in Credibility Theory (Study Note C-24-05) by Dean, C.G.
Option C
• Introduction to Credibility Theory (Third Edition), 1999, Herzog, T.N., Chapter 1-3 (background only) Chapters 4–8
Chapter 9 (background only)
*Any textbook errata are included below.
Study Notes: The # indicates new or updated material.
Code Title
Tables for Exam C/Exam 4 - Update 01.12.09
Loss Models Errata Second Edition http://www.soa.org/files/pdf/lm2e-errata%20070606.pdf Derivatives Markets, Errata, 2006 Second Edition, by R. McDonald
http://www.kellogg.northwestern.edu/faculty/mcdonald/htm/typos2e.html
Past Exams All released exam papers since 2000, can be found at:
http://www.soa.org/education/exam-req/syllabus-study-materials/edu-multiple-choice-exam.aspx
C-09-08 Exam C Sample Questions and Solutions
C-21-01 Credibility (to be used with Option B only)
C-24-05 Topics in Credibility Theory (to be used with Option B only)
C-25-07 An Introduction to Risk Measures for Actuarial Applications
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