The lecture course Finance 1 is the first in a three-semester sequence on mathematical finance. Finance 1 is meant to equip students with a basic understanding of how financial markets work and what the most fundamental techniques for pricing and hedging derivatives are.
The first half of the lecture course (Finance 1a) studies arbitrage arguments, the pricing of financial instruments like options and hedging in discrete-time (one-period and binomial multi-period) stochastic market models. The second half (Finance 1b) studies dynamic models and questions one can only answer within this class of models. We consider American options and hedging techniques in incomplete markets like super- and quantile hedging. We will also start a discussion of risk management.
Subsequent lecture courses in this module (viz. Finance 2-3) will be devoted to the economic theory of financial markets and more advanced continuous-time models, developed within classical stochastic analysis.
We follow mainly the ideas in:
Föllmer, Schied, Stochastic Finance: An Introduction in Discrete Time
Shiryaev, Probability, especially Chapter VII on Martingales