This course is part of the Mathematical Finance Master's Degree Program.
Subtitle: Obstacle Problems and Applications
Text: (1) P. Feehan, M. Poghosyan, and H. Shahgholian, ``Variational Inequalities, Obstacle Problems, and Free Boundary Problems in Economics, Finance, and Engineering", book in preparation. 2. J-F. Rodrigues, "Obstacle Problems in Mathematical Physics, North-Holland, New York, 1987.
Prerequisites: (1) An undergraduate (or higher-level) course on real analysis covering basic integration theory and the concepts of Hilbert spaces and Banach spaces; (2) A one-semester undergraduate (or higher-level) course on partial differential equations (for example, based on the text by Walter Strauss).
Description: We introduce graduate students to the theory required to understand variational inequalities, obstacle problems, and free boundary problems. They have many applications in applied mathematics, economics, engineering, and quantitative finance, including the study of constrained heating, economics, elasto-plasticity, fluid filtration in porous media, game theory, minimal surfaces, physics, optimal control, and valuation of American-style options. The intended audience includes second and higher-year doctoral and master’s level students in mathematics, engineering, mathematical finance, and materials science.