Syllabus

Title
0451 Quantitative Methods
Instructors
Assoz.Prof. PD Dr. Zehra Eksi-Altay, BSc.MSc.
Contact details
  • Type
    PI
  • Weekly hours
    2
  • Language of instruction
    Englisch
Registration
08/31/21 to 09/30/21
Registration via LPIS
Notes to the course
Subject(s) Doctoral/PhD Programs
Dates
Day Date Time Room
Tuesday 10/19/21 02:00 PM - 05:00 PM D4.0.019
Tuesday 11/02/21 02:00 PM - 05:00 PM D4.0.019
Tuesday 11/09/21 02:00 PM - 05:00 PM D4.0.019
Tuesday 11/16/21 02:00 PM - 05:00 PM D4.0.019
Tuesday 11/23/21 02:00 PM - 05:00 PM Online-Einheit
Tuesday 11/30/21 02:00 PM - 05:00 PM Online-Einheit
Tuesday 12/07/21 02:00 PM - 05:00 PM Online-Einheit
Tuesday 12/14/21 02:00 PM - 05:00 PM Online-Einheit

Contents

The course gives an introduction to the  mathematical techniques needed for quantitative finance and derivative asset analysis.

The course consists of three parts.

Part 1 (Basics):  Optimization (Background from multivariate calculus, unconstraint optimization: necessary and sufficient conditions, constraint optimization: Lagrange and KKT);  Probability background (Probability space, random variables, integration, limit theorems, measure change);  Basics for stochastic processes in discrete time (filtrations, conditional expectations, stochastic processes, sub- and super martingales)

Part 2 (Discrete time finance): Mathematical finance in discrete time (setup and self-financing trading strategies, absence of arbitrage and fundamental theorems of asset pricing,  risk neutral pricing);  Stochastic control in discrete time (Supermartingales, optional sampling theorem, optimal stopping and  American options, discrete time control and the dynamic programming (Bellmann principle))

Part 3 (Stochastic processes in continuous time and basic Ito calculus): Stochastic processes and Brownian motion (Basic notions, stopping times and optional sampling, Brownian motion and Poisson process); First and quadratic variation, pathwise Ito formula, properties of Ito integrals)

Learning outcomes

After the lecture the participants will be familiar with basic concepts in discrete and continuous time finance. In particular, they will have the necessary skills to follow scientific literature on discrete and continuous time models in finance and economics.

Attendance requirements

There is mandatory  on site (or online) attendance. This means that students should attend (online or on-site) at least 80% of all lectures ( at most one session  can be missed).

Teaching/learning method(s)

This course is mainly taught using a combination of (i) lectures elaborating relevant topics and (ii) homework assignments consolidating and expanding the knowledge  by developing solutions to applied problems.

Assessment

4 Homework assignments (25%), course participation(5%)  and an oral exam (70%).

Recommended previous knowledge and skills

Probability theory equivalent to the lecture Probability in the Master Quantitative Finance at WU

Availability of lecturer(s)

Last edited: 2021-05-03



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