Introduction to Mathematical Finance

Spring term 2022, Institute for Mathematical Sciences, Shanghaitech University

Schedule: Tuesdays and Thursdays 8:15-9:55. (15.2.22-2.6.22) Room S506 in the IMS.

Modified schedule during the pandemic prevention period: Tuesdays and Thursdays 8:30-9:50 (online classes).

In financial industry it is important to use market models for derivative pricing, in paricular for non-liquid traded derivatives. We need to understand the assumptions made on market models to be close to reality. In this course we learn about stochastic finance. We analyze arbitrage, completeness, hedging and convergence to the Black-Scholes model.

For the understanding of obstructions it is a good choice to start with the discrete time approach.

The topics we study in this course are:

• arbitrage theory

• derivatives

• complete markets

• convergence to the Black-Scholes model

• Brownian Motions and Ito-integration (basics)

• super-, submartingales and hedging

• optimal stopping times

• arbitrage theory for liquid options

• Monte Carlo integration

Textbook:

1. Stochastic finance (An introduction in discrete time), Hans Föllmer and Alexander Schied, Walter de Gruyter, Berlin, New York 2002, ISBN 3-11-017119-8

Lecture notes will be provided here: Part1 Part2.

Problem sheets: Sheet1-9 Sheet 10  Sheet 11  Sheet 12 Sheet 13