Math Actuary and Mathematics - Just how much?

[EeLoOd]

Hello-

I'm curious about the depth of mathematics which a successful actuary must know. I'm enrolled in Calculus with Single Variable, which is a general calculus class. However, there is one with Honors, in which only a few are accepted and are taught the same material but with a more rigorous manner and enhanced focus on proofs and theorems. I am just curious if I will be missing out on some important material to be used to succeed in later more mathematical subjects, or if it is just a course for those planning on pursuing graduate studies in mathematics.

Thanks in advance.

 

[chiro]

Hello-

I'm curious about the depth of mathematics which a successful actuary must know. I'm enrolled in Calculus with Single Variable, which is a general calculus class. However, there is one with Honors, in which only a few are accepted and are taught the same material but with a more rigorous manner and enhanced focus on proofs and theorems. I am just curious if I will be missing out on some important material to be used to succeed in later more mathematical subjects, or if it is just a course for those planning on pursuing graduate studies in mathematics.

Thanks in advance.

Hey EeLoOd and welcome to the forums.

As you are probably aware Actuarial Science is based statistics, financial mathematics, and business studies (business finance, economics).

If you want to be an actuary you have to sit a set of exams. The exams are in financial maths one of which is "basics" (ie bonds, interest, annuities, etc) and another in financial economics (portfolio optimization, derivatives etc).

With statistics you have an exam in foundation of stats which is basically covering any standard year long introduction to A-level stats at university level.

After these you get into specialized stats courses which are basically applications of statistics to insurance. Most actuaries work in insurance and if you don't like the idea of doing that you may want to pick something else.

So anyway the further stats courses will be things like markov modelling and solving markov systems in the context of insurance, survival tables and their use in life insurance, utility theory and their use and a lot of applications of statistics to various insurance problems.

There is also an economics exam. In australia its roughly equivalent to both first year courses in microeconomics and macroeconomics, I'm not sure what its like in other countries.

With regard to the financial math see if you can borrow the book Investment Science. It will cover a lot of the stuff you need to learn in that area.

As for actuarial statistics, the book Actuarial Mathematics by Bowers is the bible. There is also an Actex solution manual for the exercises if you get serious about going this route.

My advice to you is if you want to go the actuarial route, then don't do an actuarial science degree and do a math degree. The reason? When you are doing actuarial subjects (whether inside uni or outside uni working for a company) you will be flooded with stuff that you have to remember.

If you learn the foundations of the math you are dealing with well, its going to be a lot easier when you come to learn all of the applications. Another reason for this is that a math degree gives you options outside of actuarial applications if you don't want to go down that route (and many people that start the journey don't finish it).

With regards to subjects for preparation major in stats and you should be right. You'll have to do multivariable calculus and some differential equations, but most of the other courses are just applications of these courses (kinda like how engineering and physics is).

Final bit of advice: you should be able to download sample exam papers from the appropriate institute (UK,US,AUS etc) so that will give you a pretty damn good idea of the kind of standard you will need to meet.

Good luck!

 

[Locrian]

It depends some on your area of work, but in the majority of cases you need calculus, a little diff eq and a little linear algebra to start.

In some parts of Europe (France, I believe) much of what you need to know is taught in courses just for those purposes. The UK, on the other hand, has a set of exams that I believe are not too unlike the US exams. In the US, you take a series of tests which teach you much of the math you need to know. The tests are very difficult.

The key thing is to understand that being an actuary is a business job in which you must also know and apply some math. You are a businessperson, and professionalism is taken very seriously.

 

[Locrian]

I am just curious if I will be missing out on some important material to be used to succeed in later more mathematical subjects,

I feel confident in saying you will not miss out, though there may be lots of other reasons to take that course. If you are in the US, mention it and I'll tell you what I learned, since that is where I work as an actuary.

 

[EeLoOd]

As for actuarial statistics, the book Actuarial Mathematics by Bowers is the bible. There is also an Actex solution manual for the exercises if you get serious about going this route.

My advice to you is if you want to go the actuarial route, then don't do an actuarial science degree and do a math degree. The reason? When you are doing actuarial subjects (whether inside uni or outside uni working for a company) you will be flooded with stuff that you have to remember.

Thanks for the suggestion. Because you described the book as being the bible for actuarial mathematics, I will definitely consider it. My university does not have a formal degree program in actuarial science, but it does offer a customized "combined" major Econ/Math, usually taken by students interested in pursuing graduate studies in economics or business, or by those interested in becoming actuaries. It's good to know that I'm not the only one who thinks actuarial science is not really the best major (but still beneficial) for being actuary.

I feel confident in saying you will not miss out, though there may be lots of other reasons to take that course. If you are in the US, mention it and I'll tell you what I learned, since that is where I work as an actuary.

Thanks for answering, and yes I am in US. Any insights, comments, and/or tips will be appreciated.

 

[Locrian]

I kept putting this post off because I wanted to do it “right”, but I think that will result in me never responding. Let me throw down a few thoughts and maybe it will stir up questions or discussion.

Actuaries maintain the financial stability of the company they work for. If it was up to marketing, management and the public, insurance companies would rapidly be turned into Ponzi schemes and pillaged. This isn’t because any of those people are bad, it is just that they don’t always have a financially and mathematically sound view of the long term consequences of policies they make. In fact, if you look at the early days of insurance (early/mid 19th century) insurance companies came and went on a whim.

Society has decided that insurance is a valuable financial tool and that it requires a special kind of regulation. Actuaries are a key piece of that deal between the public and those insurance companies. Actuaries have an obligation to the companies they work for, to the professional organization they are part of, to their customers and to the state and/or federal government. These sometimes competing interests are reflected in the work actuaries do on a regular basis.

Actuaries typically work at one of two types of businesses, insurance companies or consulting companies that typically consult for insurance. There are lots of exceptions; actuaries at large accounting firms, for instance, have jobs that have attributes of both of those types.

Actuaries typically work in one of four fields (all of which contain insurance and consulting companies): Property & Casualty, Health, Life and Pension. The expected pay, type of work, number of jobs and career outlook varies for each of those. However, entry level employees don’t always have the option of choosing which field to go into; sometimes you have to start with the job you’re offered. There is another field that counts as an oddball – reinsurance. Reinsurance can be like all or none of the other fields.

What typical actuarial employers are looking for in entry level candidates: business minded individuals who can apply mathematical concepts to their daily work, pick up technical/technological skills easily and can pass the actuarial exams. That last requirement is key – a mediocre employee that can pass exams can surely be useful for some work or another, but most students who can’t pass the exams either quit or are fired, and thus they constitute a great cost with little return. Employers are wary of people they think can’t make it to a credential.

Employers typically care about (in a rough order of importance) your exams passed, your relevant work experience, applicable skills, college GPA, and college major. Don’t spend a lot of time agonizing over what degree you get; quantitative ones help, but even that isn’t necessary. A couple of exams passed and an internship or two will go very far towards getting that first job.

Actuarial work is concentrated geographically. The vast majority of jobs are in a handful of cities which are mostly located in the Northeast. There are jobs in a few smaller cities, but if you live somewhere that is not a financial center, you should count on moving. Actuarial work isn’t like nursing or accounting; there’s no work in a small rural town. At least, no work you’d want.

I got my job two and a half years ago or so and have really enjoyed it. I got lucky; I work in a small department in a medium (a few thousand employees) sized company, so I see a wide variety of work and it tends to have a lot of impact. Actuaries here have three key properties that make us special – we have a mathematical background, we have a wide variety of technical skills and we have a deep understanding of the business. Lots of other departments have people with two of those, but very few have many with all three, so we get many varying requests. I regularly have output that goes straight to the officers or the board of directors, and I can see the impact of my contributions companywide. I think I enjoy this more than I would reserving all day, but it’s hard to know without having actually done it.

I also enjoy our department culture. I can’t stress enough that actuarial work is business work, but underneath their professionalism actuaries tend to be an odd crew and that works well for me. The probability of making a nerdy math or D&D joke and having someone get it is high in this department, and near zero in most other ones.

One last note – you asked and others often ask about what math to know. Ultimately the exams teach you most of the actuarial mathematics you need to know. But I’d like to comment that what I’ve found is that the most important mathematical skills are easy to learn and hard to apply. Probability and statistics can be devious in a way that differential equations never seemed to me. Often correct values are difficult to explain; forecasts can be wrong because they were done; trends act in ways that defy common sense. The world can be weird, and you can’t ever let it catch you off guard, because people will notice.