Which methods are used by actuaries in practice?
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.
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.