This lecture and its sequel ``Advanced topics in analysis H'' are aimed at those wishing to learn about both the basic mathematical concepts and the overall picture of mathematical finance.
First, we begin from the single and multi-term binomial setting. The following notions, arbitrage pricing, martingale measures, the 1st fundamental theorem, and complete markets are discussed in the setting. Martingales in the discrete time setting play an essential role.
Understanding the important notion and ideas of option pricing theory in discrete time models.
Supplies the basis for the sequel ``Advanced topics in analysis H''.
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||Introduction: Pricing and Hedging/binomial models/option prices(1)||Details will be provided each class session.|
|Class 2||Martingale Measures(discrete time)-1: Discrete time market model/Trading strategies/Risk neutral pricing/Black-Scholes formula|
|Class 3||Martingale Measures(discrete time)-2: Risk neutral pricing/Black-Scholes formula|
|Class 4||The 1st fundamental theorem(1): The separating hyperplane theorem/construction of martingale measure|
|Class 5||The 1st fundamental theorem(2): Geometric interpretation of the theoreml/Generalization|
|Class 6||Complete markets(1): martingale representation/completeness|
|Class 7||Complete markets(2): Incompleteness|
|Class 8||American options|
None in particular.
J. Sekine, ``Mathematical Finance'', Baifukan (in Japanese)
D. Williams, ``Probability with Martingales'', Cambridge
R. J. Elliott and P. E. Kopp, ``Mathematics of Financial Markets'', Springer
Based on reports. Details will be provided in the class.
None in particular
None in particular