The Mathematics of Financial Risk Management

University of Toronto, Canada

Luis A. Seco, Department of Mathematics, University of Toronto, Toronto, Canada

Since the ground breaking work of Nobel Laureates Markowitz, Black, Scholes and Merton, mathematics has emerged as the leading discipline to address fundamental questions in finance. After the success of the pricing theories in the early nineties, risk management, which deals with related but fundamentally different issues, is attracting a great deal of attention in the academic community triggering its increasing protagonism in the banking, as well as in the insurance and utility industry. This course is intended to be an introduction to the issues of current interest (academic as well as industrial) targeted to students as well as senior scientists.

The course will consist of two separate parts.

Part I. Mathematical Finance. This part will deal with standard elementary materials, which serve as a goal in itself as well as for background for Part II. No previous knowledge of the area is assumed. The level will be elementary.

Part II. Risk Management. This part will deal with the issues of Value-at-Risk and credit risk, and will have a practical point of view, stressing current industry practices. Level will be advanced. Everything will be covered in detail.

Part I: Introductory. Part II: Intermediate to advance.

The course is intended for students and scientists with little or no previous knowledge in the field. Attendees will obtain a broad view of the mathematical content of modern finance, learn the basic concepts, and have a clear picture of the issues of current industrial interest and of its mathematical undertones.

Students and scientists with little or no previous knowledge in the field.

Undergraduate probability, measure theory and statistics, elementary Fourier analysis, some knowledge of differential equations.

Dr. Luis A. Seco is Director of RiskLab-Toronto, a mathematical finance laboratory located at the University of Toronto which conducts research in mathematical finance and risk-management in partnership with Algorithmics Inc. and in cooperation with the local financial industry. His recent research has concentrated mainly in the study of Value-at-Risk. Prior to that, he was a mathematical physicist studying the structure of large atomic systems, for which he was awarded the Sloan and Connaught Fellowships, as well as awards from the NATO Science Division. He is a frequent collaborator of Algorithmics Inc., Bank of Nova Scotia, Bank of Montreal, and Refco Futures Canada Ltd.

8:00 Registration

8:30-9:30 Introduction to Pricing Theories

- One step
- Multi-step
- Continuous time
- Option pricing

9:30-10:00 Interest Rate Theory

10:00-10:30 Coffee - Wilson Hall Cafeteria

10:30-11:00 Interest Rate Theory (continued)

11:00-12:00 Portfolio Theory

- Markowitz mean variance model
- Scenario Optimization for portfolio selection

12:00-2:00 Lunch - Wilson Hall Cafeteria

2:00-3:00 Approximate Pricing Theories

- Replication
- Monte Carlo
- Analytic methods

3:00-3:30 Coffee - Exhibit Hall, Wetmore

3:30-4:30 Value-at-Risk

- Direct methods
- Asymptotic methods

4:30-5:30 Credit Risk

- One step
- Multistep
- Implied default probabilities

5:30 Short course adjourns

Seats are limited. We urge attendees to register in advance. To register for either short course, please submit the preregistration form on page. Upon completion, return the form with your payment to reach the SIAM office on or before June 23,1998.

This short course will be in Room 1016 Wilson Hall; the morning coffee break and lunch will be in the Cafeteria, Wilson Hall. The afternoon coffee break will be in the Exhibit Hall of Wetmore Hall, New College.

TJF Created: 1/21/98, MMD Updated: 5/27/98