My Background and Your Prerequisites
This post is the first in a series about studying for Actuarial Exam LTAM — Long-Term Actuarial Mathematics. This exam is basically equivalent to the exam previously labeled Exam MLC — Models for Life Contingencies.
Back in the year 2005, I studied for and passed actuarial Exams P and FM (Exams 1 and 2), on probability and on financial mathematics. Actually, I did not spend much time studying for Exam P because I had already taught a course on probability.
At the time, however, I was not very familiar with financial mathematics beyond the basics of compound interest. Because of this, I did spend quite a lot of time studying for Exam FM.
I tell my students at Bethel University to practice problems for these exams so much that they become second nature. I held myself to this standard as I worked to become familiar with the subject, its terminology, and its notation.
What I Did Between 2005 and 2019
Between the years 2005 and 2019 I had many other projects that I pursued. I put actuarial science aside for much of that time (except for a research project I did with a student). I was working on developing teaching materials for differential equations, multivariable calculus, and complex analysis. A couple articles I wrote based on these efforts were: (1) “Teaching an Online Sophomore-Level Differential Equations Class with Mathematica Supplements” (CODEE Journal) and (2) “Using Modules in Teaching Complex Analysis” (PRIMUS). My biggest project during this time was the development of content for my YouTube channel, “Bill Kinney Math” (yes, my creativity in name-choice was lacking).
As I emphasized above, most of my initial videos on YouTube were related to differential equations, multivariable calculus, and complex analysis. After a few years I transitioned into videos on statistics, real analysis, and abstract algebra. However, by far the largest number of videos were about financial mathematics. I have made almost two-hundred videos on the subject in the last couple years.
Current Sabbatical
I am currently on sabbatical for the first five months of 2019. This fact, coupled with a flexible summer teaching schedule, means that I have a lot of time during the first eight months of 2019 to get back into actuarial science. During the first three months of 2019, I started this blog and have so far included a lot of content on financial mathematics. In the last week, I have also started to create YouTube and blog content on probability.
However, I am most interested in studying to take actuarial Exam LTAM. Since my video-making schedule will continue to be focused on Exam P and Exam FM content, I will most likely just blog about this at the moment. On the other hand, I won’t rule out sharing some of this content on YouTube when I run across something extra-interesting. I will probably also advertise some of my blog content about Exam LTAM with short videos on YouTube.
I should say that much of the Exam LTAM content is material I am already somewhat familiar with. In fact, the basics of this material formed the foundation of the research project that I did with a student. I am still waiting to find out if an article we wrote about this project will be published in a certain journal. I will let you know when we hear back about it.
The familiarity I have with Exam LTAM content is why I am pursuing blogging about this subject right now. If I were going in the recommended order, I would blog about Exam IFM — Investments and Financial Markets. This is something I hope to do in the future.
Your Prerequisites
What kind of background will you need to understand the content of Exam LTAM? There are two main foundational subjects: probability (Exam P) and financial mathematics (Exam FM). Of course, calculus is an important prerequisite for both of these areas.
Within probability, the most important ideas to understand are probably the basics of discrete and continuous random variables. You should know the meaning of and be able to work with probability mass functions (PMFs), probability density functions (PDFs), and cumulative distribution functions (CDFs). You should know how to find probabilities, means, medians, variances, and standard deviations. Conditional probability is also important to understand. Finally, it is important to understand how to deal with random variables that are transformed versions of other random variables.
From financial mathematics, the foundational content on present and future values and on annuities are probably the most valuable parts. Of course, the ability to work with geometric series is always valuable for this.
Finally, you should realize that actuarial notation is a big stumbling-block for many people. It is convenient and efficient, but it is very imposing. Some memorization will probably be necessary for it to truly sink-in.
My Resources
Just for your information, the textbook resources that I have and will make use of are: (1) “Actuarial Mathematics“, 2nd Edition, by Bowers, Gerber, Hickman, Jones, and Nesbitt; (2) “Models for Quantifying Risk“, 4th Edition, by Cunningham, Herzog, and London; and (3) “Actuarial Mathematics for Life Contingent Risks“, 2nd Edition, by Dickson, Hardy, and Waters.
The last of these three resources is the one featured on the Society of Actuaries (SOA) syllabus for exam LTAM. It is the newest one of the three and probably the one I will focus on using the most.