PhD in Mathematics – Concentration in Actuarial Science and Risk Analytics

PhD in Mathematics – Concentration in Actuarial Science and Risk Analytics

This PhD concentration is intended for students with strong quantitative skills who want to acquire advanced analytical tools for academic careers and research and development careers in insurance, consulting, investment, pension, healthcare, banking and financial services.

The University of Illinois is an ideal place for education and research in actuarial, financial and risk management, due to its well-established system of interdisciplinary collaborations among various units. Highlights of the University’s achievements in these areas can be found here. Based in the renowned Department of Mathematics, this program offers a unique blend of a world-class rigorous mathematical education with practical research and professional training in actuarial science, quantitative finance and risk analytics. Read more at our poster for graduate studies in actuarial science and risk management.

PhD candidates cover most of the material for professional exams, and build on that foundation to receive in-depth education on modern techniques and challenges in the financial, actuarial and risk management professions through coursework, seminars, internships and research. Due to the interdisciplinary nature of actuarial and financial research, PhD candidates are encouraged to broaden their knowledge by taking courses in statistics, finance, insurance, risk management, data analytics, etc.

The Department of Mathematics offers a unique multi-year internship program where PhD candidates are encouraged and supported to receive internship experience in summer breaks during their PhD studies. More information can be found here. There are also internship opportunities on campus at the University of Illinois Research Park. Students are also exposed regularly to cutting-edge research development in industry and academia by attending and presenting at the Actuarial Science and Financial Mathematics Seminar, where a wide range of prominent researchers are invited to speak and visit. In addition, students can participate in the seminar series on Mathematical Finance, Risk and Uncertainty, jointly organized with the Department of Industrial and Enterprise Systems Engineering.

Our program offers opportunities for PhD candidates to work in a wide range of research areas, including stochastic analysis in actuarial and financial modeling, quantitative risk management of equity-linked insurance, pension and social security, industry solvency assessment, collective risk theory, Monte Carlo simulations, and more. The Illinois Risk Lab also provides a channel for practical research to address emerging problems from industrial partners and professional organizations.

Financial support is offered for up to six years to every student admitted to our PhD program, in the form of teaching assistantships, research assistantships and corporate-sponsored fellowships. We also provide full reimbursement of exam fees for those who choose to take professional exams. To help students develop communication and networking skills, we also provide financial support for PhD candidate to travel to research summer schools and conferences in related areas.

Admissions Requirements

Students with a Bachelor’s degree in any quantitative field can apply directly to the PhD program. Applicants are expected to demonstrate competence in real analysis, linear algebra, and probability and statistics, either through undergraduate coursework or by means of Graduate Record Examination (GRE) mathematics subject test.


Complete information regarding graduation requirements can be found in the Guide for Graduate Students in Mathematics. The following list only serves as a summary for prospective students.

PhD candidates in this concentration are required to complete the core courses:
MATH 540 (Real Analysis)
MATH 561 (Theory of Probability I)
MATH 563 (Risk Modeling and Analysis)
STAT 510 (Mathematical Statistics I)
One additional course from a list of approved core courses for all PhD students.

PhD candidates in this concentration must also demonstrate competence in three additional supporting courses:
MATH 564 (Applied Stochastic Processes)
STAT 425 (Applied Regression and Design)
FIN 591 (Theory of Finance)

and in two of the following actuarial graduate courses:
MATH 565 (Actuarial Models for Life Contingencies)
MATH 567 (Actuarial Models for Financial Economics)
MATH 568 (Actuarial Loss Models)

Although not required, many PhD candidates in the Actuarial Science and Risk Analytics Concentration take elective courses in functional analysis, partial differential equations, linear and nonlinear programming, multivariate analysis, statistical computing, macro and micro economics, portfolio management, predictive modeling, machine learning.

How to Apply

The application process for this concentration is the same as the regular Mathematics PhD program. Detailed instruction as well as general requirements can be found here. Candidates should clearly identify the Actuarial Science and Risk Analytics Concentration on the application form, and in their personal statement.

Frequently Asked Questions

If I want to become a practicing actuary, should I consider PhD education in Actuarial Science?

The actuarial profession in North America highly values professional credentials obtained through passing professional exams with credentialing bodies such as the Society of Actuaries and Casualty Actuarial Society. A PhD education in Actuarial Science is not a necessary component for a career path as an actuary. Students who are interested in career paths in traditional actuarial roles should pursue our MS program in Actuarial Science. The PhD concentration prepares students for academic careers and research and development offices/departments in the insurance and financial service industries. For example, a graduate may find a tenure-system position in a university, work as a quantitative reinsurance analyst, a catastrophe modeling analyst, a quantitative strategy researcher in a proprietary trading firm, and so on.

What qualifications are you looking for in admissions?

A typical PhD applicant should have a bachelor’s degree or its equivalent in a quantitative field, including but not limited to pure mathematics, applied mathematics, statistics, engineering, quantitative finance, physics, etc. Students should take the GRE General test.

How much do GRE scores get weighted into the application of a prospective student? What other factors weigh the most in an application?

We consider the whole application to find students with sufficient preparation and motivation to succeed in our program. Applicants typically perform strongly on the GRE General exam (80th percentile and above on the quantitative portion, and we like to see good scores on the other sections too). Scores on the GRE Mathematics subject exam (if taken) vary quite widely. Coursework relevant to actuarial science and risk analytics is valuable. 

The transcripts from your bachelor’s and master’s institutions are important. We pay close attention to courses and grades. If you come in with an actuarial or financial mathematics background, we do consider your track record of passing professional exams. However, students in this concentration also come from other quantitative fields.

What funding is available to students?

All admitted students are offered a full tuition waiver, and a teaching assistantship (the stipend is $20,000 for the academic year; most students get some summer funding too). The funding offer runs for 5 or 6 years, depending on your level of preparation. Fellowship and RA support is available to some continuing students who perform strongly in the program.

How do the requirements for those pursuing the Actuarial Science emphasis differ from those pursuing other fields of study?

Notably, students in the Actuarial Science and Risk Analytics Concentration are not required to take Math 500 Abstract Algebra. Instead, they take Stat 510 Mathematical Statistics I. The full requirements for students in the Concentration are listed here.

What should be my focus to prepare for this program beyond admissions?

Take as much undergraduate real analysis as possible (called “advanced calculus” at some universities), and tackle the hardest problems you can get your hands on. Learn metric space topology, with normed vector spaces being an important example. Get familiar with spherical coordinates, the divergence theorem (Gauss theorem), and Green’s first and second identities.

Real analysis lays the foundation for probability, stochastic processes, and differential equations, at the graduate level. If you are strong in real analysis, then you can learn and pass the material in the first year comprehensive courses in a PhD program like ours.