In this lecture the students will deepen their understanding of various aspects of continuous-time models in financial mathematics. In the first part of the lecture we will take a deeper look at the underlying tools from stochastic calculus. In particular we will discuss stochastic integration  and the Girsanov theorem.  These concepts will then be applied to study derivative asset analysis in generalized Black-Scholes models. In the final  part of the lecture we will give an introduction to term-structure modelling and to stochastic optimization.

This course deepens the understanding of continuous-time finance and it  covers a number of advanced topics of Continuous Time Finance.

The aim of this course is to:

• obtain a basic understanding of the main topics, such as stochastic calculus for Brownian motion, financial mathematics in continuous time and applications
• understand and describe the properties of competing term-structure models, change of numéraire techniques and basic stochastic control.

After completing this course the student will also:

• have deepened his/her ability for teamwork
• be able to formulate essential problems of CTF 2 and propose possible solutions in a precise way (that is in a mathematical rigorous way. This skill is different from a purely intuitive understanding of the topics of this course).

Full attendance is compulsory. This means that students should attend at least 80% of all lectures, at most one lecture can be missed.

• 45% final  exam (format tbd)
• 30% completion of work sheets (remote take home)
• 25% presentation

Passing the  final examination is necessary to pass the course.