How mathematical objects bridge random walks and modern finance
This lecture from Oxford University's third-year mathematics course explores the fundamental structures of probability. Watch as Jan Obloj demonstrates how advanced concepts like martingales and conditional expectation provide the essential tools for solving complex problems across diverse scientific contexts.
The lecture serves as an introduction to the 'Probability, Measure and Martingales' course, highlighting the utility of key mathematical objects. It examines how techniques such as martingale transforms and changes of measure can be applied to varied scenarios, including the asymptotic behavior of a simple symmetric random walk and the Galton-Watson branching process.
Beyond pure theory, the presentation connects these abstract concepts to practical applications, specifically the problem of hedging a claim within mathematical finance. By showcasing these connections, the lecture establishes the necessary foundation for the rigorous mathematical work required in the subsequent stages of the course.
Source: Probability, Measure and Martingales: an introduction - Oxford Mathematics 3rd Year Student Lecture
