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Recently I read a comment from an actuary that a lot of the math they studied as part of the program they never actually used.

I'm not interested in becoming an actuary, but I'm interested in learning more about some of the methods that are commonly used (mainly in non life insurance). Can anyone clarify which statistical / mathematical methods are commonly used by actuaries or insurance analysts in their day to day work?

Is there a big emphasis on bayesian methods such as bayesian credibility? What about more traditional methods such as the chain ladder method. Or perhaps Markov chain methods for no claims discounts?

I've looked at a couple of books such as Hossack, Pollard. Introductory statistics with applications in general insurance (seems like a good basic book) and

Boland. Statistical and probabilistic methods in actuarial science (claims to be a practical books with useful R code, but is actually full of theorems, proofs, and lemmas).

but I've no idea whether it is worth expending the effort in wading through a book like Boland's in terms of practical knowledge acquired. I tried to find a introductory book that would take an applied approach that mixed theory with analyzing actual datasets using something like SAS or R, but I was unsuccessful.

So can anyone clarify which methods are used on a regular basis by working actuaries. Any book recommendations would also be appreciated. Thanks.

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  • $\begingroup$ I think if you look at the separate certs on the SOA web site, you will get an idea of what areas are important (when you get passed the math exams) for ASA, CERA and FSA. See: soa.org/education/exam-req. Also, you might want to look at some of the programs at the universities they cite and look at the courses and books for said programs and courses, see: soa.org/Education/Resources/default.aspx $\endgroup$
    – Amzoti
    Commented Nov 27, 2012 at 2:18

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I worked for a few years as life actuary. They study syllabus was a bit different then vs. as I vaguely understand it now. In that era, one studied math courses to become an associate of the Society of Actuaries. Then you studied the actual machinations of the insurance business to become a Fellow.

Passing exams was a key factor in your pay scale which was a plus or a minus depending on results. But for sure, one's career track is heavily dependent on these results.

But, in short, I can tell you that I never used one iota of the math covered on the exams. They are more of a training ground to come up with fast ways to solve problems. The higher level exams require a good deal or practice and are high-pressure considering what is at stake. As an example of the intensity, I got a 10 (out of 10) on the risk theory exam (considered a tough one) answering 7 out of 15 questions - and I yet may have gotten some wrong.

The major function of actuaries was to calculate and substantiate the adequacy of reserves. This relied heavily on mortality tables - an easy math problem. A significant aspect of the endeavor entailed accounting regulations both for GAAP and state of domicile statutory requirements.

Most of the actual work in this regard was modeling of various policy lines. And each company has it's own set of well- worn models.

A latter consideration was the requirement of cash flow testing. This again was a modeling problem as the investment assets had to be tested for their performance under various, usually extreme, interest rate scenarios. This was intended to make sure there is money available to fund the reserves.

So while passing exams entailed cubic splines, the Poisson distribution, the Black-Scholes model, Ito's Lemma, the real work required familiarity with insurance regulations and their related accounting treatment.

For more information on the study materials, esp. books, you can go to the websites of the Society of Actuaries and the Casualty Actuarial Society.

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  • $\begingroup$ Thanks for the comprehensive response. That was very informative. $\endgroup$
    – Antonio2011a
    Commented Nov 28, 2012 at 4:39
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I have interned as an actuary in a property and casualty insurance company in the United States and will soon start working as an actuary. I am not an expert but I've talked to quite a lot of people and asked questions and I know the basics of the exam system for the Casualty Actuarial Society. So, I know a few things.

Yes, I have heard that much of what you learn on the exams is not used. But, some of the later exams are used. For example, Exam 5 is called Basic Techniques for Ratemaking and Estimating Claim Liabilities. It teaches you how to do pricing and how to do reserving. These are probably done by different actuaries at most company. And, the text that is used for this is freely available on the CAS website here. None of the math is very complicated at all. And, yes the chain ladder method is part of what is used for reserving as far as I know. But, there are other techniques.

There is also Exam 8 which is called Advanced Ratemaking. I don't know much about this one but I know it covers generalized linear models somewhat and I also know that I have heard many people talk about generalized linear models. At my company, I have talked to one person in charge of a research department and generalized linear models seems to be one of the most important things they use. If you want to see the exact books needed to study for this exam, see here and scroll down toward the bottom.

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  • $\begingroup$ Thanks for the links, I'll check out those resources. $\endgroup$
    – Antonio2011a
    Commented Nov 28, 2012 at 4:38
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Actuaries don't practice anything very different from methods in probability theory. They are mostly focussed on processes, typically Poisson (accidents typically follow that distribution).

Some useful books are listed here

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  • $\begingroup$ The level of knowledge required about the statistical processes being used in actuarial settings, at least from what I have seen, are usually set at an advanced programme mathematics course in the final year of high school, e.g. Poisson/exponential models. Sure, if you are going to construct your own life tables you may need more advanced statistics, but most actuaries just use the information already available to them. The mathematics from the actuarial exams does, however, help one understand underlying distributions and enables one to explain potential anomalies. $\endgroup$
    – Aaa
    Commented Sep 13, 2013 at 18:26
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Read this Abstract: Actuarial Methods in Health Insurance Provisioning, Pricing and Forecasting By Peter Lurie

  1. OSC Valuations/ChainLadder
  2. PPCI/IBNR
  3. Loss Ratio/BF
  4. PCE (Classical Statistical Regression Methods:
  5. Pricing & 6. Forecasting are in Methods 1-4, Hence determination of Reserves is to calculate the future claims/prices or forward pricing (as an insurer you want to cover future pricing costs). Simply they calculate the Estimates: (1) Projects Costs, (2) Losses/Loss Ratios, (3) Claims (Outstanding Claims, IBNR, PPCI and Development Claims).
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