This lecture and its sequel ``Advanced topics in analysis H1'' are aimed at those wishing to learn about the basic mathematical concepts of mathematical finance. The following notions, continuous time martingales, Brownian motion, stochastic integral, stochastic differential equations, and the Black-Scholes model are discussed in these two lectures. In this lecture we start from the introduction of stochastic processes, develop the theory of martingales, and introduce the definition of the Brownian motion.
Students are expected that they understand the basic notions of continuous time martingales and Brownian motion.
Mathematical Finance, Martingale(discrete time)
✔ Specialist skills | Intercultural skills | Communication skills | Critical thinking skills | Practical and/or problem-solving skills |
Blackboard and handouts
Course schedule | Required learning | |
---|---|---|
Class 1 | Probability theory | Details will be provided during each class session |
Class 2 | stochastic processes | |
Class 3 | discrete time martingale | |
Class 4 | Doob's inequality/Stopping time/Optional Sampling theorem | |
Class 5 | Martingale | |
Class 6 | Quadratic Variation | |
Class 7 | Brownian Motion(1) | |
Class 8 | Browninan Motion(2) |
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D. Williams, ``Probability with Martingales'', Cambridge
R. J. Elliott and P. E. Kopp, ``Mathematics of Financial Markets'', Springer
N. Ikeda, S. Watanabe, "Stochastic Differential Equations and Diffusion Processes", North Holland
Based on reports.
None in particular
syoiti.ninomiya+AG[at]gmail.com
None in particular