• The binomial model and the no-arbitrage asset pricing.
• Complete and incomplete markets.
• Optimal investment strategies.
• Pricing of path-dependent options.
• The Brownian Motion as the limit of the symmetric random walk.
• Basic continuous time models.

The course’s main subject is to study the fundamental principles of mathematical modeling of some of the basic financial problems, such as the pricing in complete and incomplete markets and the optimization of the investment portfolio. The main part of the course material is dedicated to discrete time models. At the first two weeks, we will introduce the basic probabilistic continuous time models and analyze some of their applications.

After the successful completion of the course a student will be able to:
• Understand the mathematical tools that are needed for the modeling and the analysis of the valuation and the portfolio selection problems.
• Develop and reproduce the basic valuation and pricing models with real data.
• Study the related scientific literature and understand the basic principles of risk measurement and management in markets of financial derivatives.

Autonomous work
Team work
Work in inter-scientific environment

Writing exams (90%) that refers to the theoretical questions and exercises on the material developed in the class.

Howemorks (10%) that ask students to solve some related to the course exercises.

The main textbook (not required though) is the “Stochastic Finance, Vol. 1”, of Steve Shreve.