Friday, 25 November 2011

Actuarial joke


A guy walks into a butcher's shop looking for something for his dinner. Sitting in the refrigerator are two piles of what looks like brains. The customer turns to the butcher and says to him "What are these in the refrigerator?"
The butcher replies that the plate on the left contains accountants brains, which he is selling for $1 a pound and the other contains actuaries brains which he will sell for 10 cents a pound.
The customer is quite surprised at hearing that actuaries brains were so cheap, as he always thought actuaries were highly intellegent people, so he asked the butcher about the discrepancy.
The butcher replies "Yeah, but have you any idea how hard it is to find accountants brains?"

Sunday, 13 November 2011

Inspirational article


By Andrew Lin

This article is reprinted from the May 2010 Actuary of the Future newsletter.

“How…and why did you do all this?”

Ever since I obtained the FSA designation at age 20, that’s certainly one of the most frequent questions I get asked (well, that and, of course, the “what exactly is an actuary?”). It’s safe to say it’s indeed a legitimate question considering that being an actuary isn’t exactly the most well-known or popular occupation. Ask most high school or college kids what they want to be and chances are that the usual reply will consist of “a doctor,” “a lawyer,” “an engineer,” “no freaking clue”, or something along those lines. So, how did I get this far? That’s a good question.

It was my uncle who first enlightened me on what an actuary really is. Becoming an actuary sounded fantastic—good pay, relatively low stress, normal work hours, being able to apply technical skills toward business—or that was how it was first described to me. At the time, though, I really didn’t think much of it. I had been busy with classes, extra-curricular activities, and, you guessed it, studying for the dreaded SAT—everything that would help get me into a good college, which I thought was a more practical goal. To me, the actuarial exams were this set of professional exams that just seemed way out of my league in terms of intellectual capabilities. Perhaps the exams might have been a realistic goal for a high school math genius or whatnot, but me? No way.

It was only after all the college-aspiring commitments that I finally decided to take my tradition to the next level; my tradition of always doing extra, learning at my own pace, and taking on what’s challenging to me. Having always been interested in economics and mathematics, the actuarial exams seemed like the logical course to pursue. After all, what was the harm? It was with that mentality that I began my four-year journey immersed in exam studying…still, the decision was hardly an impulsive one.

I have always had this hobby of reading non-school related materials right before bed every night. At first it was fascinating Chinese history stories that most of my elementary school peers avoided at all costs (I mean what normal kid would choose history books over comic books? Am I right?).  Gradually, it progressed to more serious Chinese literary works which I came to appreciate immensely. After I came to the United States though, I was forced to give those up for arduous hours of learning English. For nine consecutive months, I learned 25 vocabulary words a day without skipping a single day. Pretty crazy, I know. This habit carried itself over into college when the actuarial exams became my new focus.

You might be wondering, “Where does an 18-year-old get this kind of motivation?” As cheesy as it may sound, I think it was pretty much an inner determination of striving to be better. I’ve always believed that I should live life as hard as I can, and become the best that I can be. I never really thought I was exceptionally smart, but I always worked hard. I’d love to say I’ve been the perfect student my entire life, but that would definitely be a lie. I grew up in Taiwan, where schools all have a class ranking system, even at the elementary level. At the start of school, I ranked 33 (not bad, eh?)…out of a class of 35. Six years of hard work later, I pulled myself up and graduated 10th. I also remember attending after-school English-improvement courses where the policy was either to pass the exams or risk being kicked out of class, a brink I precariously neared on multiple occasions, even after retaking exams. With hard work and perseverance though, I was able to rise to the top of the entire class two years later. When high school rolled around, I moved from Taiwan to Los Angeles. Again, I had to fight an uphill battle. I was initially forced to take the easiest classes available because of my language limitation. Four years later, I graduated with 12 AP credits, a feat which aided me in graduating college in three years.

Steve Nash, one of my all-time favorite basketball players, once said, “If every basketball player worked as hard as I do, I’d be out of a job.”  (For the record though, I’m a Lakers fan.) I believe the same could be said of how I came to become the youngest actuary, and really everything that I’ve done up to this point. So while most other college students partied hard and drank even harder, I skipped the festivities and became a frequent visitor to the school library. Yes, even on Friday and Saturday nights. Sad huh? In retrospect, I suppose I missed out on the typical college life most people experience, only to replace it with exam studying and job searching. Many people have asked if I have any regrets in that regard. My response is: not really (all right, maybe just a tiny bit, but hey, life’s all about sacrifices right?). Though, I should add that I definitely did enough crazily stupid things in high school to compensate for my college life or lack thereof. Given the choice to go back in time, there’s nothing that I would change. I’d make the same choices again in a heartbeat.

With every passing score, I developed not only more confidence in myself, but also more interest in these topics. I got to a point where I just didn’t want to stop. The challenge from the FSA exams drove me to follow through, even though many people kept warning me that finishing all the exams too early may not be the best of ideas. It’s always been my goal in life to try to understand as much as possible of how the world operates. The FSA exams allowed me to not only integrate the technical knowledge from the preliminary exams, but also gain a broad understanding of how many areas of the financial markets work—I was just fascinated.

You would think that after passing all these exams, I would be sure of becoming an actuary. In reality though, even at the point when I finished all the preliminary exams, I still wasn’t certain if I really wanted to be an actuary. I had just viewed the exams as a sort of challenge to myself. It only slowly began to hit me that all this could turn into a career. I learned a lot at my internship at Transamerica in my freshman year, but the position seemed a little too laid-back to me, especially while many of my peers were entering investment banking and working ridiculous hours for higher pay. Later, it was my internship in the annuity hedging department at Prudential that really caught my interest, as it allowed me to apply much of what I learned from the exams. As it turned out, an actuary’s job is precisely what had been described to me by my uncle—well paid, relatively low stress, normal hours, and most importantly, interesting (that is, for a mathematics/business-oriented person). The experience definitely helped me to finally decide to work as an actuary.

The funny thing is, I have to admit that what was holding me back from working as an actuary was actually the normal hours that comes with it (a bit of the post-exam-emptiness syndrome, I suppose). Having always worked harder than my peers, it made me uncomfortable to think that there are people working 80 hours a week out there while I’m only working 40. Ultimately though, I’ve concluded that even if I’m not working 16 hours a day for some company, I can still utilize my time well and learn on my own. Some of my hard work has already begun to pay off, as I gradually come to realize that I do possess a lot of knowledge often unknown to many around my age. I’ve achieved all this by doing extra work on my own, not through being pushed to work hard. So I took on the less-grueling, yet just as interesting and challenging route, and went back to Prudential after I graduated. I have not regretted my decision, as the job has taught me much and provided me with opportunities to meet amazing people as well as challenging problems to solve. I by no means have even scraped the surface of being an actuary. I’m learning every day on the job, from those who have long been in the field and possess invaluable experience. I still have much more to learn as an actuary and I will certainly give it my all to be worthy of being “the youngest actuary.” As for my habit of persistently taking those extra steps, they’ve carried on after I started working—I continue to read a lot in my free time. I feel pretty content with life. I feel like I really am growing, both as an actuary and as a person.

Will I always be an actuary in the traditional sense? I have no idea. But the experience—the challenge from each exam, all the great people I get to meet along the way, the amount of knowledge gained—I would never exchange it for anything. I will always carry the “FSA" title after my name with the greatest sense of pride.

Andrew Lin, FSA, is a senior actuarial analyst at Prudential.

Saturday, 12 November 2011

Binomial Approximation


A Bin(n,p) distribution is the sum of n Bernoulli variables, so the Central Limit Theorem says that it will approximate to a Normal distribution if n is large enough. n could be a few dozen, less for a symmetrical distribution and more for a very non-symmetrical distribution.


For the Poisson distribution E[X] = var[X] = μ. A Bin(n,p) distribution has E[X] = np and var[X] = npq. So for a Binomial distribution to approximate to a Poisson distribution np ≈ npq, i.e. q ≈ 1. For example, if n = 1000 and p = 0.01, then E[X] = 10 and var[X] = 9.9, and a Poi(10) distribution could be considered as an approximation, depending on any other relevant criteria.


The Bin(n,p) distribution has an upper limit of n, while neither the Normal nor Poisson distributions have an upper limit.

Memoryless Property


Basically it means the distribution doesn't know where it is on the curve. Formally P(X > a | X > a-b) = P(X > b)
The only dists in CT3 with this property are exponential and geometric.
eg. if X~Exp then P(X>4 | X>3) = P(X>1).

Hypothesis Testing


Suppose our null hypothesis is that the mean age of students = 22 and our alternative hypothesis is that the mean age is not equal to 22.

Suppose we take a sample and find that the sample mean age is 26.

We can deal with this in two main ways:

(1) What is the probability of getting this sample result if Ho is true? This is called the probability method and the probability is called the p-value.

(2) What value of the sample mean would convince me that Ho is true/false? This is called the critical value method.

Using (1), we can calculate the probabilty of getting a sample mean as extreme as this on both sides (ie >26 or <18) if the population mean is actually 22. Suppose this probability turns out to be large, eg 34%. We would say that getting a sample mean as extreme as this if the population mean is actually 22 is not very unusual at all so therefore we would say that we do not have sufficient evidence to reject Ho. However, if the probability of getting a sample mean as extreme as this if the population mean is actually 22 is very low, eg 3%, we would say that this is very unusual and therefore we would reject Ho.

We usually use 5% as a cut-off point, ie we usually run a 5% Type I error - so there is a 5% chance of rejecting Ho when it is in fact true. This is called the significance level of the test.

Using (2) we can determine the critical values of the sample mean, C1 and C2 (or the test statistic, eg Z1 and Z2) such that the probability of a result lower than C1 or higher than C2 is 5%. Then if our sample mean (or the test statistic) is in this critical range, we will reject Ho at the 5% level.

Negative Binomial Distribution


Differences between Type I and Type II Negative Binomial Distribution and how to identify which is it?
Type 1 counts the number of trials up to and including the kth success.

Type 2 counts the failures before the kth success.

So suppose we are counting the number of goals we score (success) for the penalty kicks we make (trials).

Suppose we score our 3rd goal on our 10th penalty kick.

Under Type 1 X=10 as it is the 10th kick when we got our 3rd goal.

Under Type 2 X=7 as we had 7 failures before we got our 3rd goal.

In CT3 our default choice will be a type 1 (for CT6 it will be type 2).

Source -Nick Campbell

Actuarial KPO


Actuaries are highly skilled professionals and are in great demand in insurance industry all over the world. Due to recently privatised industry here in India , first wave of qualified actuaries will be out within two years. By that time number of Actuarial Students will also be quite large.

KPO - Knowledge Process Outsourcing industry in india is growing rapidly. Since Actuaries all over the world are in great demand and India promises to provide skilled manpower to cater this need. KPO industry in india ( in actuarial field) promises to be a big employer and money spinner in coming 5 years.

Many IT companies have already sensed this oppurtunity and already started to stablish their KPO's. Other big multinational insurance company also have started to offshore their Actuarial Work to Indian subsidary.

Lets see how this industry fair in the future.

Actuaries in General Insurance


Actuary in General Insurance companies generally performs two very important tasks.

1. Reserving.
2. Premium Rating.

In reserving an actuary suggests company how much IBNR(incurred but not reported) claims could come in future along with how much reserves company should keep to take care of IBNER. moreover Actuary also gives his opinion on Solvency position of the company.

In Premium Rating , an actuary uses past data and trends to come up with rates which should be charged to policy holders in order to be competitive and profitable in the markets. These rates are dependent on rating factors and trends shown by the industry and companies past data.

Although the scope of actuary in General insurance company is much more than these two tasks, but currently in India , Actuaries perform these tasks only. Further the way in which IRDA is developing the market , it is not long when an actuary starts to perform other activities which are performed all around the globe.

Actuarial science jobs


Being an actuary, you can be employed in various fields.

Life Insurance Companies

General Insurance Companies

KPO Companies (Knowledge Process Outsourcing)

Consulting companies

Investment Companies

Pension and Benefits Companies

Health Insurance Companies

Reinsurance Companies

In India, Life Insurance, KPO and Consulting companies provide large portion of the actuarial demand. Further, General Insurance sector after de-tariffing promises to provide very lucrative job profile in near future.

Pension and Benefits field is also likely to benefit given the reforms that are taking place in Pension and related areas. It is heard that Banking and Financial Companies are also now hiring actuaries for analyzing risks.

Health insurance actuaries are also in great demand, given that in India the scope of Medical Insurance is tremendous and lot of companies around the world want to enter India as soon as possible. Demand for health actuaries are bound to increase.

I don't know for sure, but talking with various industry experts, there is a feeling that work of General insurance or Health actuary involves more subjective decision. Due to this fact the responsibility of their decision is high and thus they are paid more than a life or pension actuary all around the world. Although in India General insurance or Health insurance companies are not paying as industry standard across world but it is likely to change soon.

List of Life insurers in India

Bajaj Allianz Life Insurance Company
Birla Sun Life Insurance Company
HDFC Standard Life Insurance Company
ICICI Prudential Life Insurance
ING Vysya Life Insurance Company
Life Insurance Corporation of India
Max New York Life Insurance Company
Met Life India Insurance Company
Kotak Mahindra Old Mutual Life Insurance
SBI Life Insurance Company
TATA AIG Life Insurance Company
Reliance Life Insurance Company
Aviva Life Insurance Company
Sahara India Life Insurance Company
Shriram Life Insurance Company
Bharti Axa Life Insurance Company
Future Generali India Life Insurance Company
IDBI Fortis Life Insurance Company
Canara HSBC Oriental Bank of Commerce Life Insurance Company
Aegon Religare Life Insurance Company
DLF Pramerica Life Insurance Company


List of Non-Life insurers in India

Bajaj Allianz General Insurance Company
ICICI Lombard General Insurance Company
IFFCO Tokio General Insurance Company
National Insurance Company
The New India Assurance Company
The Oriental Insurance Company
Reliance General Insurance Company
Royal Sundaram Alliance Insurance Company
Tata AIG General Insurance Company
United India Insurance Company
Cholamandalam MS General Insurance Company
HDFC ERGO General Insurance Company
Export Credit Guarantee Corporation of India
Agriculture Insurance Company of India
Star Health and Allied Insurance Company
Apollo DKV Insurance Company
Future Generali India Insurance Company
Universal Sompo General Insurance Company
Shriram General Insurance Company
Bharti AXA General Insurance Company
Raheja QBE General Insurance Company ( Prospective)
List is taken from site of IRDA.

Young actuaries in india

Source- IANS
Once considered the exclusive preserve of venerable middle-aged executives, the office actuaries -- experts who scientifically review the risks in the life and non-life insurance business -- is getting younger by the year.
"Earlier, Indian actuaries in the age bracket of around 45 years were hired to head the offices," said G.L.N. Sarma, the managing director of Hannover Re Consulting Services India, speaking about these experts who assess the financial impact of future events.
"But in the recent times the age of recruits for the top post has come down to around 35 years," Sarma, who in 2007 was himself named actuary at Bharti Axa Life Insurance at the age of 36, told the media.
As per Insurance Regulatory and Development Authority's (IRDA) regulations, every life and non-life insurer should have an appointed actuary. While life insurers should have a permanent official, non-life companies can have a part timer.
Currently, there are 24 non-life insurance companies in India, six of which are state-run, and 23 life insurers, one of which is owned by the government -- Life Insurance Corp.
Against this, there are just 216 qualified actuaries who are members of the Institute of Actuatries of India and practise within the country, 76 of whom are under the age of 40. In addition, there are 46 other fellows in all age group who are overseas.
R. Kannan, member-actuary, at the regulatory authority, said only four non-life insures have full-time appointed actuaries and others have part-timers, many of them over 70 years of age. But the situation is changing now.
Some of the recent additions to the growing young-appointed or chief actuaries club are Tania Chakrabarti at the Royal Sundaram Alliance General Insurance Company, Sharon D' Costa at the SBI General Insurance and Abhay Tewari at Edelweiss Tokio Life Insurance.
In terms of pay packets, appointed actuaries are highly paid professionals commanding an annual price of around Rs.5-7 million on the life side and slightly lower in the general insurance sector. Expat actuaries command premium price.
Further, appointed actuaries are IRDA's representatives in the insurance companies and hence can't be hired or fired without the regulator's consent. One of the youngest in the insurance industry is 30-year-old science graduate Sharon D'Costa of SBI General.
"I found actuarial science interesting and decided to pursue the course and complete it in five years," D'Costa told IANS.
On the other hand, 35-year-old Tania Chakrabarti, who holds a master's in quantitative economics from Indian Statistical Institute, Kolkata, and working with the Murugappa group, found actuarial science a logical progression.
Clearing the exams in 2009, she became the appointed actuary of Royal Sundaram Alliance General Insurance Company in June 2010. Some of the other young actuaries are Anil Kumar Singh of Bajaj Allianz Life and Ashley Edward Rebello of HDFC Standard Life.
According to the institute, it takes at least four years to complete the course as some subjects are practical-oriented, needing actual work experience.
With not many new life insurers on the Indian horizon and the existing ones downsizing their actuarial departments, the non-life insurance sector is now turning lucrative for the young actuaries, say industry officials.
"Non-life companies are becoming more aware of the value that full time actuaries with a strong actuarial department can bring to the organisation in product development, pricing, financial planning and portfolio performance analysis," Chakrabarti said.
"IRDA has over the last few years strengthened the statutory reporting requirement from appointed actuaries in non-life industry bringing it closer to that of life segment. It will become increasingly difficult for a part-time actuary to cope with the pressures."
Ajay Bimbhet, managing director of Royal Sundaram, agreed and said there is the need for greater statutory reporting, and scrapping of state-determined pricing in the motor and commercial business; only a full-time actuary can improve profitability.
"Non-life offers more challenge to actuaries as the products have to be priced based on risks. The market is more evolving now and there are more regulatory requirements," SBI General's D'Costa added.
According to the Institute of Actuaries of India (IAI) - the professional body for actuaries - 87 of the 170 actuaries in India as on March 31, 2010, are in the age bracket of 26-45 years. (IANS)

Actuarial pickup lines


 1. My love for you is endless, like a perpetuity.
2.. Since the first time I saw you, my interest in you has compounded continuously.
3.. I love the way your hairline emulates the p.d.f. of the Gamma distribution.
4.. If you put 5 red, 4 yellow, and 3 green balls in an urn, what's the probability of you coming home with me tonight?
5.Of course I won't tell anyone. I'm like the exponential distribution, I have the memoryless property.

Source-www.actuarialjokes.com