Convex Optimization in Quantitative Finance

Abstract

We give many examples of problems in quantitative finance that can be solved using convex optimization. The examples are simple, but readily extended to more practical versions that include additional objective terms or constraints. For each example we give CVXPY code, illustrating how simple it is to specify and solve the convex problems.

About the Speaker

Prof. Stephen P. BOYD received an AB degree in Mathematics, summa cum laude, from Harvard University in 1980, and a PhD in Electrical Engineering & Computer Sciences from the University of California, Berkeley in 1985. In 1985 he joined the faculty of Stanford University’s Electrical Engineering Department. He is currently the Samsung Professor of Engineering, Professor of Electrical Engineering, and a member of the Institute for Computational and Mathematical Engineering at Stanford. 

Prof. Boyd’s research focus is on convex optimization applications in control, signal processing, machine learning, and finance. He is the author of many research articles and four books: Introduction to Applied Linear Algebra: Vectors, Matrices, and Least-Squares (with Lieven VANDENBERGHE, 2018), Convex Optimization (with Lieven VANDENBERGHE, 2004), Linear Matrix Inequalities in System and Control Theory (with L. El GHAOUI, E. FERON, and V. BALAKRISHNAN, 1994), and Linear Controller Design: Limits of Performance (with Craig BARRATT, 1991). His group has produced many open source tools, including CVX (with Michael GRANT), CVXPY (with Steven DIAMOND), Convex.jl (with Madeleine UDELL and others), and CVXR (with Anqi FU and A. NARASIMHAN), widely used parser-solvers for convex optimization. His group's CVXGEN software is used in many applications, including the SpaceX Falcon 9 landing system.

Prof. Boyd has received many awards and honors for his research in control systems engineering and optimization, including a Young Investigator Award from the Office of Naval Research, a Presidential Young Investigator Award from the US National Science Foundation, and the Donald P. Eckman Award from the American Automatic Control Council (AACC). In 2012, he was awarded the Mathematical Optimization Society's Beale-Orchard-Hays Award with Michael Grant, given every three years for excellence in computational mathematical programming. In 2013, he received the IEEE Control Systems Award, given for outstanding contributions to control systems engineering, science, or technology. In 2023, he was given the AACC Richard E. Bellman Control Heritage Award, the highest recognition of professional achievement for US control systems engineers and scientists. He is a Fellow of the IEEE, SIAM, INFORMS, and IFAC, a Distinguished Lecturer of the IEEE Control Systems Society, a member of the US National Academy of Engineering, a foreign member of the Chinese Academy of Engineering, and a foreign member of the National Academy of Engineering of Korea. 
 

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