Entry requirements

Probability theory MN1, Inference theory MN1,

Introduction to scientific programming MN1 and

Numeric analysis MN1. Markov processes MN1 is

recommended.

Aims

The aim of the course is to provide an introduction

to modern mathematical theory of asset pricing,

portfolio optimisation and risk management in

financial markets.

Content

Basic concepts in finance: present value, interest

rates, compounding, annuities. Portfolio

optimisation: Markowitz' model, quadratic

programming, risk evaluation, optimisation methods.

Arbitrage theory and asset pricing. Overview of

financial derivatives: options, futures, swaps,

exotic options. Black-Scholes model. Overview of

hedging, risk management and portfolio insurance.

Each topic will be covered in three stages:

motivation from the point of view of financial

markets, mathematical theory and computer-assisted

numerical solutions of the underlying problems.

Instruction

Lectures and laboratory sessions.

Assessment

Written and, possibly, oral examination at the end

of the course. Moreover, compulsory

assignments may be given during the course.