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


  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.


Last problem sheets: Sheet 10  Sheet 11  Sheet 12


New problem sheet: Sheet 13


Prof. Daniel Skodllerack


Shanghaitech University

Institute for Mathematical Sciences,  Room S413


Office hours: There are no official office hours because of the pandemic situation. We can arrange an office hour. Please get in contact with me via email or wechat.

Email address:  dskodlerack at



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© Daniel Skodlerack 上海科技大学 数学科学研究所 上海市浦东新区华夏中路393号上海科技大学创艺学院南楼(D区)室S413