university of waterloo phd mathematics

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Welcome to Ruodu Wang's Homepage

Ruodu Wang, Ph.D.

Canada research chair in quantitative risk management, professor of actuarial science and quantitative finance.

Department of Statistics and Actuarial Science University of Waterloo

Fellow, Institute of Mathematical Statistics

Google Scholar page Curriculum Vitae Short Bio

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Research areas

- Statistics - Probability - Actuarial Science - Financial Engineering - Operations Research - Quantitative Risk Management - Economic Theory

Current research support

Canada Research Chairs (CRC-2022-00141)

Natural Sciences and Engineering Research Council of Canada (RGPIN-2024-03728)

Affiliated member

RiskLab , Department of Mathematics, ETH Zurich

My Erdös number: 3

Ruodu Wang - Ričardas Zitikis - Endre Csáki - Paul Erdös

Current teaching - Winter 2024

- ACTSC 964 Foundations of Quantitative Risk Management -->       STAT 946 - Topics in Statistics -->

This site was last updated on May 14, 2024

Recent working paper series

Ruodu wang's suggestions for writing mathematics in scientific papers, my group members: current and past phd students and postdocs, wikipedia page on e-values, online seminar series: weekly seminars on risk management and actuarial science, an interview with ruodu wang in expanding horizons (nov 2021) by the society of actuaries.

Department of Statistics and Actuarial Science University of Waterloo Mathematics 3, 200 University Avenue West Waterloo, Ontario, Canada N2L 3G1

Office: M3 3122 Tel: (519) 888-4567 ext. 31569 Email: wang (at) uwaterloo.ca Profile at the Department website

Editorial Duties

Available positions.

A few postdoctoral and PhD positions in Actuarial Science , Mathematical Finance , Statistics , or Risk Management are currently available in the Department of Statistics and Actuarial Science at the University of Waterloo. For potential research topics, see Publications and Research .

Interested junior scholars and students are welcome to send an email inquiry directly to me. For the postdoctoral positions, applications should be submitted on mathjobs via this link .

Selected Publications by Area

Please see the Publications tab for a full list and pdf files of manuscripts. Co-authors are in [brackets].

Department of Statistics and Actuarial Science, University of Waterloo School of Mathematics, Georgia Tech School of Mathematical Sciences, Peking University Risklab Switzerland, ETH Zurich Institute of Mathematical Statistics (IMS) Society of Actuaries (SOA) Statistical Society of Canada (SSC) Natural Sciences and Engineering Research Council of Canada (NSERC) Dependence Modeling, an open access journal European Actuarial Journal ASTIN Bulletin - The Journal of the International Actuarial Association An interview with Ruodu Wang (by SOA, 2021) Wikipedia page on e-values

April 26, 2024

My past PhD student Qiuqi Wang won the 2024 Pierre Robillard Award for the best PhD thesis in probability or statistics defended at a Canadian university during 2023. See the news from the Statistical Society of Canada .

March 5, 2024

February 20, 2024

The suggestions for writing mathematics document has been updated.

December 30, 2023

Happy new year of 2024! Our paper "Robustness in the optimization of risk measures" receives the Best Paper Award on Financial Engineering in Operations Research from INFORMS.

Department of Statistics and Actuarial Science University of Waterloo Mathematics 3, 200 University Avenue West Waterloo, Ontario, Canada N2L 3G1 Office: M3 3122 Tel: (519) 888-4567 ext. 31569 Email: wang (at) uwaterloo.ca

Recently Accepted Papers (10)

Recent conferences organized.

Workshop on Risk Measurement and Regulatory Issues in Business , Montreal, Canada, September 11-14, 2017

Workshop on Random Complex Structures and Data Analysis in Finance , Beijing, China, August 3-7, 2016

The 4th Workshop on Insurance Mathematics With a Special Session on Longevity and Pension Risks , Waterloo, Canada, February 5-6, 2016

Upcoming Events

The 4th Workshop on Insurance Mathematics With a Special Session on Longevity and Pension Risks , February 5-6, 2016

Pre-publication Manuscripts

Please, critical comments on these papers are very much appreciated.

Temporary Address (Fall 2015)

RiskLab Department of Mathematics ETH Zurich 0892 Zurich, Switzerland Office: HG G39.5

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Mathematics: Find papers

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Mathematics research databases

Find mathematical research and papers using these research databases.

• MathSciNet Articles in mathematics, computer science, statistics, and econometrics, as well as applications to science and engineering. Coverage: 1940 - present more... less... Produced by the American Mathematical Society, MathSciNet provides reviews, with abstracts, to the world's literature in mathematics and related areas. MathSciNet is compiled from the print equivalents, Mathematical Reviews and Current Mathematical Publications. Reviews are classified according to the Mathematics Subject Classification.
• MathSciNet QuickStart Guide
• zbMATH Open zbMATH Open (formerly known as Zentralblatt MATH) indexes research in pure and applied mathematics. more... less... From the European Mathematical Society (EMS), the Heidelberg Academy of Sciences and Humanities, and FIZ Karlsruhe, zbMATH Open contains around 4.2 million bibliographic entries with reviews or abstracts drawn from more than 3,000 journals and book series, and some 190,000 books. Coverage starts in the 18th century, is complete from 1868 to the present day, due to the integration of the "Jahrbuch über die Fortschritte der Mathematik" database. zbMATH Open has been available as an open access database since January 2021.
• HAL: Hyper Articles en Ligne "HAL is a multidisciplinary open access archive for the deposit and dissemination of scientific research papers, whether they are published or not, and for PhD dissertations. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers."

These database have research and papers relating to more specific areas within mathematics.

• Cryptology ePrint Archive "The Cryptology ePrint Archive provides rapid access to recent research in cryptology. Papers have been placed here by the authors and did not undergo any refereeing process other than verifying that the work seems to be within the scope of cryptology and meets some minimal acceptance criteria and publishing conditions."
• Database of Actuarial Research Enquiry "The Database of Actuarial Research (DARE) contains over 5,000 records, including full-text journal articles and book citations, on actuarial science research in the property-casualty fields. Everything that CAS has published appears here plus more from outside organizations."
• Optimization Online "A repository of e-prints about optimization and related topics."
• Risk.net This resource has risk management articles relating to the measurement, modelling and management of financial risks; in-depth coverage of the markets across the derivative, interest rate, credit, foreign exchange and structured products asset classes; and news and analysis on the content and implications of regulation.
• SAGE Research Methods Find books, encyclopedia and dictionaries about research methods. Coverage: varies more... less... SAGE Research Methods provides a tool called Method Maps, which visualizes relationships among more than 700 unique methods terms, concepts and people. Method List can be used to compile selected books, book chapters and journal articles for later review or sharing with colleagues. Note: Waterloo only gets the text (read: eBook/reference work) content from Sage Research Methods. Waterloo subscription to SAGE Research Methods doesn't include SAGE videos.

Multidisciplinary research databases

Not sure where to start? The databases below cover many disciplines including math, business, economics, health, life science, physical science, and technology.

• Scopus Peer-reviewed literature from scientific journals, books and conference proceedings, covering the fields of science, technology, medicine, social sciences, and arts and humanities. Coverage: 1966 - present
• Web of Science Articles and citations in the sciences, social sciences, arts, and humanities. Coverage: Varies more... less... Web of Science is comprised of several databases. The Science Citation Index Expanded (SCI) covers journals in the medical, physical and natural sciences, and engineering fields. The entire database extends back to 1899. The Social Sciences Citation Index (SSCI) covers journals in the social sciences. The entire database extends back to 1898. The Arts & Humanities Citation Index (AHCI) covers journals in the arts and humanities. It also selectively covers relevant items from science and technical journals. The entire database extends back to 1975.
• Google Scholar Google Scholar is a search engine finds scholarly information from many sources (however, not everything in Google Scholar is scholarly). To access materials paid for by your library, go to Google Scholar, then choose Settings and click "Library Links" to add the University of Waterloo. more... less... Google Scholar is a search engine that emphasizes scholarly information, particularly in the sciences and technology. It draws from academic publishers, professional societies, preprint repositories and universities. Note: Access To access materials paid for by your library, go to Google Scholar, then choose Settings and click "Library Links." The off-campus user will first need to login via "Get access from anywhere."
• arXiv A pre-print server which hosts papers (that have not been peer reviewed) relating to physics, mathematics, computer science, nonlinear sciences, qualitative biology and statistics Coverage: 1991 - present
• JSTOR Provides access to back issues of journals in the humanities, social sciences, and physical sciences, many of which date from the 1800s. Coverage: varies (excludes current 3 to 5 years)
• ProQuest A platform with many databases of journal indexes and abstracts, as well as some with full text Coverage: Varies more... less... This online platform hosts multiple resources.
• EBSCOhost A platform with many databases of journal indexes and abstracts, as well as some with full text Coverage: varies more... less... This online platform hosts multiple resources. Note: Offline digital lending: Requires Adobe Digital Editions.

Finding research databases for other disciplines

• Research guides at Waterloo Guides are created for each department on campus and list subject resources for each discipline. Find research in Computer Science, Engineering, Physics, Biology, Business, Psychology, Education, and more.
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Abbreviated c.v.

Recent developments, publications.

For a full publication list, please see my Google Scholar page .

Research interests

Graduate students and thesis titles, other projects.

Doctor of Philosophy (PhD) in Applied Mathematics - Water

The Graduate Studies Academic Calendar is updated 3 times per year, at the start of each academic term (January 1, May 1, September 1). Graduate Studies Academic Calendars from previous terms can be found in the archives .

Students are responsible for reviewing the general information and regulations section of the Graduate Studies Academic Calendar.

Program information

Admission requirements, degree requirements.

• Collaborative
• Minimum grade point average: 78% or its equivalent.
• It is absolutely essential that the application for admission into the program contain evidence of potential for performing original research. This should be provided by successful completion of a Master’s thesis in a mathematics-related discipline.
• In some circumstances a student enrolled in the MMath program may transfer to the PhD program without completing their MMath program.
• Supplementary information form
• Transcript(s)
• Number of references:  3

normally from academic sources.

• English language proficiency (ELP) (if applicable)

Thesis option:

The program of studies of a PhD student is directed by a PhD Advisory Committee consisting of the supervisor(s) and two other faculty members. This committee should be approved (by the graduate officer) within three terms of enrollment. At least one of the two other members should be from (or cross-appointed to) the Department, and one of the members should be from outside the research group of the supervisor(s).

• Graduate Academic Integrity Module (Graduate AIM)
• Students must complete 4 one-term (0.50 unit) graduate courses after the Master's degree, satisfying a breadth requirement and Water core course requirement, or 8 one-term (0.50 unit) graduate courses after the Bachelor's degree, satisfying a breadth requirement and Water core course requirement. Candidates for the PhD degree must maintain a grade point average of at least 70% in their coursework. Besides the breadth and Water requirements, there are no other constraints on course selection.
• AMATH 740 Numerical Analysis
• AMATH 741 Numerical Solution of Partial Differential Equations
• AMATH 751 Advanced Ordinary Differential Equations
• AMATH 753 Advanced Partial Differential Equations
• AMATH 777 Stochastic Processes in the Physical Sciences
• AMATH 731 Applied Functional Analysis
• AMATH 732 Asymptotic Analysis and Perturbation Theory
• This degree is offered through the Collaborative Water Program. This program, jointly offered by a range of departments across several academic faculties, promotes the development of interdisciplinary perspectives on water. Collaborative Water Program students complete their specialist training in their respective home departments, while working with colleagues from a variety of other departments in core interdisciplinary courses (WATER 601 and WATER 602)
• WATER 601 Integrated Water Management
• WATER 602 Integrated Water Management Project
• 1 graduate level water course from outside the student’s home Faculty agreed to by the student’s Supervisor and the Collaborative Water Program Director.
• Students may not count more than 1 graduate course that is cross-listed with an undergraduate course for credit towards their PhD degree. This restriction applies to all 600-level AMATH courses and any cross-listed courses offered by other departments. Note: students who transfer directly into the PhD program (without completing the Master's degree) may take up to 2 cross-listed courses.
• If a PhD student has taken an equivalent course during a Master's program, this can be counted (upon approval from the Graduate Officer) towards completion of the breadth requirement but does not reduce the number of courses required.
• Courses are selected in consultation with the student's supervisor. Students are encouraged to select courses that will help them develop a broad knowledge of Mathematics and its applications: appropriate courses are often offered by other departments in the Faculties of Mathematics, Science and Engineering.
• Link(s) to courses
• Applied Mathematics (AMATH) courses
• Water (WATER) courses
• Collaborative Research Seminar I
• Students are required to present a seminar on their thesis or major paper research proposal and, if appropriate, early stage results to current and past Water students and Water Institute faculty members. Seminars will normally occur following the completion of WATER 601 and WATER 602. Seminars will provide the opportunity for students to discuss how learnings from Water courses were applied in, or influenced, research proposals or research work in the student’s home department. Seminars will normally be poster presentations at Water Institute organized events. The seminar is not an oral examination of the thesis or paper; rather, its purpose is to develop the student's ability to communicate their research in an organized and informative manner.
• Collaborative Research Seminar II

Students who have completed the Collaborative Research Seminar 1 as part of their Masters Water degree, must complete the Collaborative Research Seminar 2.

Students are required to present a seminar on their PhD thesis proposal to current and past water students and Water Institute faculty members. Seminars will normally occur following the completion of required courses and the comprehensive exam. Seminars should present how learnings from the Collaborative Water Program were applied in, or influenced, thesis proposals. Seminars will normally be poster presentations or talks at Water Institute organized events. The seminar is not an oral examination of the thesis proposal; rather, its purpose is to develop the student's ability to communicate their research in an organized and informative manner.

• Collaborative Academic Contribution

Students who have completed the Collaborative Water Program Research Seminar 1 as part of their Masters Water degree, must complete the Collaborative Academic Contribution milestone.

Students are required to make an academic contribution to the Collaborative Water Program. The proposed contribution will be documented by the student and approved by the student’s Supervisor and the Collaborative Water Program Director. Potential contributions may include, but not be limited to:

Development of new or improved curricula or course content;

Delivery of a lecture(s);

Preparation of a publication;

Preparation of a case study;

Mentorship of a group of students.

• PhD Comprehensive Examination
• Comprehensive examination purpose: Consistent with University-level minimum requirements.
• Timing: Consistent with University-level minimum requirements. 
• Committee: Consistent with University-level minimum requirements. Note: The Faculty of Mathematics wishes to use the option to have the committee approved by a delegate of the Associate Dean, namely by the Graduate Officer in the home department of the student.
• Who Chairs an examination: Consistent with University-level minimum requirements.
• Format / Content: Consistent with University-level minimum requirements.
• Academic integrity: In the Faculty of Mathematics, when a student needs to submit a written document to their comprehensive examination committee prior to the examination, they are required to sign an acknowledgement form affirming their work does not violate the University policy on Academic Integrity. Students are also encouraged to use a plagiarism detection software and include its report with the submission of their written document. Furthermore, the comprehensive examination committee may require the student to use such software and include the report it generated with the submission of their written component.
• During the third term of enrollment, the candidate will give a 30-minute pre-comprehensive seminar on the proposed research area, emphasizing background material. Shortly thereafter the advisory committee shall decide on the background topics that will comprise the candidate's comprehensive exam. The student will be informed of the areas of examination 3-4 months prior to the comprehensive examination.
• The comprehensive examination is to be completed by the end of the student’s fifth term. The candidate will prepare a written research proposal (approximately 25 pages) that will be submitted to the members of the advisory committee and the examination chair (normally the graduate officer) at least two weeks prior to the comprehensive examination. The proposal should describe the research problem, together with motivation, literature review, an indication of methodology, any progress made to date, and a research plan with timeline.
• Shortly before the comprehensive examination, the examination chair (through the graduate coordinator) will consult with the advisory committee to determine whether the committee wishes the exam to proceed and, if so, whether the committee wishes to meet to discuss the questions to be asked on background material. Each committee member will provide a typeset list of questions to the graduate coordinator four business days before the exam (about 3-5 questions, which can all be answered at a whiteboard in about 15 minutes). This list of questions will be provided to the candidate one hour prior to the start of the exam. The candidate will use this time to prepare answers, with no access to outside materials.
• The examination will consist of a 20 minute presentation of the proposed research followed by two rounds of questions: the first on the prepared background questions, the second on the research proposal and the relevant literature. Each examiner shall question the candidate for approximately 15 minutes in each round. If there is more than one supervisor, they will share the allotted 15 minute time-slot. The comprehensive examination should normally be completed in two hours, after which the committee will consider the student’s progress to date, the proposal, and the student’s performance in the exam. Students who have not satisfactorily completed the comprehensive examination by the end of the fifth term will have their progress reviewed by the Departmental Graduate Chair.
• PhD Lecturing Requirement
• This requirement is normally met by teaching a one-term undergraduate course, usually at the first or second year level, under the supervision of a faculty member. Students will satisfy this requirement after completing the comprehensive examination and after obtaining experience as a teaching assistant. If the department is unable to provide the student with a suitable undergraduate course to teach, the requirement may be met by giving a series of lectures of an introductory nature concerning the student's field of research.
• The program of study should have a substantial focus on water. A PhD thesis contains original results that warrant publication in the research literature. Indeed, candidates are encouraged to publish papers based on their research before submitting their theses. Moreover, the Department expects a PhD thesis to be a scholarly work that is broad in scope. As such, it should contain a discussion of the history of the research problem and an analysis of the relevant literature. For University guidelines on co-authored material in PhD theses please visit the Graduate Studies and Postdoctoral Affairs website ; additional departmental guidelines apply.
• The candidate shall defend the thesis in an oral examination before an Examining Committee, which shall consist of the Advisory Committee, one faculty member from outside the Department, and an external examiner familiar with the student's research field.

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Master of Mathematics for Teachers

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The Master of Mathematics for Teachers (MMT) program offers teachers the unique opportunity to deepen their understanding of the core foundations of mathematics — online and at their own pace. Designed to strengthen teachers’ knowledge of mathematics and its applications, the MMT combines flexibility with world-class education to deliver a rich learning experience. The program equips graduates to engage their students with renewed confidence and enthusiasm.

MMT at a Glance

This fully online program is designed for secondary-school teachers who wish to:

• Grow their understanding of the mathematical foundations of core secondary-school curricula
• Discover exciting applications of mathematics like cryptography and music
• Explore new and innovative ways to bring their knowledge into the classroom

Program Overview

Purpose and audience.

The primary focus of the MMT program is mathematics and its applications rather than pedagogy. Some of the material and tasks in each course will be directly applicable to daily classroom teaching, but much is intended to build teachers’ confidence in mathematics by strengthening their knowledge base.

This program is designed for secondary-school mathematics teachers. The focus on the secondary-school mathematics curriculum might also make the program a good fit for other educators who teach secondary school-level math. It’s expected that applicants will have been away from formal education for several years at the time of enrollment.

Teachers from around the world enroll in the MMT.

Delivery and Timing

The MMT is a fully online professional program offered on a part-time basis. Almost all required coursework is asynchronous. Due to the sequence of courses offered, students begin the program in September.

Students typically complete the program in three years, but depending on students’ needs, the MMT can be completed more quickly or more slowly.

Students complete the equivalent of nine full-term courses, including a project-based capstone. Out of these courses, only the equivalent of three full-term courses are required. Students have the flexibility to choose the remainder of their courses from the program’s course offerings.

Students in the MMT program benefit from the strength and breadth of the University of Waterloo’s world-renowned Faculty of Mathematics and the Centre for Education in Mathematics and Computing, Canada’s leader in mathematics education outreach. Our faculty are experienced, award-winning educators with a passion for mathematics and computer science education.

Here are just some of the courses we offer:

• Problem Solving and Mathematical Discovery
• Foundations of Calculus
• History of Mathematics
• Number Theory for Teachers
• Cryptography
• Statistics for Teachers
• Mathematics for Global Citizens
• Math and Music

To see the courses that we anticipate offering over the next two years, visit MMT Courses .

Tuition is now $1085.00 for a full-term course and $542.50 for a half-term course. Students can expect to pay under $1200.00 CAD per course, which includes fees and the cost of textbooks and other materials. To graduate, students complete the equivalent of nine full-term courses. See the University of Waterloo’s graduate program tuition for more information.

Many Canadian residents qualify for a tax break. Please consult the Canada Revenue Agency .

We encourage all students to inquire with their tax authority as well as their school board or Ministry of Education (or the equivalent) about any tax benefits that may result from participation in the program or any professional development subsidies that may offset or cover its cost.

Scholarships

• MMT Indigenous Scholarships ( application form )
• Agibcona Award ( application form )
• Scotiabank MMT Scholarship ( application form )

Scholarship applicants may contact us if the program application fee is a concern.

• MMT Indigenous Scholarships (submit application form by May 1, 2023)
• Agibcona Award (submit application form by June 1, 2023)
• Scotiabank MMT Scholarship (submit application form by May 1, 2023)

Admissions Criteria

• Hold a four-year degree (or equivalent) with sufficient university-level mathematical background (normally at least three or four university-level mathematics courses).
• Have at least one year of prior work experience in education, with preference given to those actively teaching in mathematics, science or computer science at the time of application.
• Provide certification of English language proficiency through one of the accepted examinations if they have not completed three or more years of post-secondary work at a Canadian institution or at an institution at which English was the primary language of instruction, or if they have not been employed for a similar period of time in a position in which English was the primary language of business.

Application Process

There is one admission cycle per year. The application deadline is June 15 and students must begin the program in September due to the sequence of courses offered.

Applicants must apply through the University of Waterloo’s online application process. Visit Applying to the MMT to learn how to apply and about the documentation required.

“The professors delivering the courses were excellent and extremely available and understanding of the wide range of backgrounds of their students. . . . I am a more confident teacher since starting the MMT and find myself often referring to what I have learned.” — MMT Graduate, Whitehorse, Yukon

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