## Learning outcome

Introductory Mathematical Finance is a semi-intensive course that equips the students with the foundation of financial modeling in a single and multi-period trading framework. The focus is on the rigorous understanding of the principle of finance merged into the model aimed at the pricing of financial derivatives. The students will be learning about pricing and hedging financial derivatives and will learn the basis of utility optimization and optimal portfolios.

At the end of the course the students will:

1. Have a good understanding of the foundation of financial modeling in a single and a multi-period trading model

2. Be able to define arbitrage and understand the concept of fair pricing

3. Be able to distinguish between complete and incomplete markets and what makes the difference

4. Be able to find no-arbitrage prices of any feasible financial derivative using the no-arbitrage principle

5. Be able to find hedging strategies of feasible financial derivatives

6. Be able to solve optimal portfolio problems in single and multiperiod markets

Besides, the students will be equipped with some universal mathematical tools:

1. Stochastic processes and the information flow

2. Probability measures, probability distributions, and changes of probabilities: risk-neutral measures

3. Expectations and conditional expectations

4. Martingales

5. Stochastic optimal control problems