John Holmes - Teaching

Courses taught at OSU:

Math 3589 Introduction to financial mathematics

Math 5194-A Stochastic calculus for financial mathematics I
I developed this graduate level course at The Ohio State University which begins with measure theory and integration, derives Browning motion from a simple random walk, and then derives the continuous time asset pricing model of Black and Scholes. The majority of the course is spent introducing and proving the necessary background material from stochastic calculus. This was a mixed course of undergraduates and graduate students.

Math 5194-B Stochastic calculus for financial mathematics II
I developed this course; a continuation of the above course. We use the tools from stochastic calculus to price a variety of American and exotic options in continuous time. We then evaluate a number of interest rate models, and finally we introduce the mathematics necessary to understand stochastic calculus when the underlying measure is a jump diffusion process. We also learned numerical methods for solving PDEs, and implemented these methods to price exotic options.

Actuarial Science and Math Finance:

I am the director of the graduate program in actuarial science and quantitative risk management. This is a unique degree which is at the intersection of actuarial science and mathematical finance. These areas, historically, have been linked very closely. Though recently the actuarial science profession has moved a little away from mathematical finance, there is a great deal of overlap in terms of tools and techniques. Our industry connections strongly value interdisciplinary programs such as ours, and we expect that demand for such programs will continue to grow. Our graduate program is an extension of our extremely successful undergraduate majors in these areas.

The actuarial science major within the math department is one of the most popular majors at OSU. There is no doubt that this is in part due to the fact that actuarial scientist is often rated as one of the best jobs in the United States. It doesn't hurt that the salary range for actuarial scientists is probably the highest among all undergraduate majors; maybe starting salaries in some of the engineering majors beat us.

Math finance is a closely related major, though geared a little more towards students interested in the finance industry. Students interested in quantitative finance will most likely need to earn a graduate degree as well.

A great source to compare career prospects across majors is DataUSA. According to them, average salaries for actuaries in the US is about $175k, and about $290k for math majors in finance.

Math Alliance:

The National Alliance for Doctoral Studies in the Mathematical Science, known as the Math Alliance, is an organization dedicated to supporting underrepresented groups in the mathematical sciences. It is filled with a huge amount of information and resources for all students thinking about pursuing a graduate degree. It also has a lot of information for early career students, even freshman. If you are an undergraduate student I highly recommend you look through the material on their website for information on how to apply to REU's, jobs in industry, and graduate school. There is also a mentor-mentee program which can link you to an established professor at another university who is interested in helping you succeed.

COMAP competition:

The Consortium for Mathematics and its Applications (COMAP) competition is an annual competition for undergraduate students in mathematics and related fields. It takes place over a weekend in the spring semester, usually towards the end of February. This competition is as much a writing competition as it is a math contest. Indeed, it is unlike other math competitions like the Putnam exam.

Students in teams of two or three, are given a choice of six problems to consider. These problems are often motivated by real world situations or events, and typically have a policy recommendation component to them. An example may be, "What is the most efficient way to evacuate southern Florida in the event of a hurricane?" or "How do we best mitigate the spread of lime disease?". Students are expected to use whatever mathematical tools they are familiar with to model and analyze the problem, and include as many real world issues as possible. Over the weekend, they will write a roughly 20 page report which will be read and graded by a panel of judges. The winning teams earn a substantial cash prize.

Math-to-industry:

Krystal Taylor founded the math to industry seminar series at OSU in 2017. If you are a student who likes math, but is unsure about careers your major may be preparing you for, I highly encourage you to attend the seminars which can be found here. You will also find a variety of useful tips and information about potential jobs and industries interested in students and recent graduates with degrees in mathematics.