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Finanzmathematik und Stochastische Integration / Mathematical Finance and Stochastic Integration (V:FinMathStochInt) (060203)- Dozent/in
- Prof. Dr. Sören Christensen
- Angaben
- Vorlesung, 4 SWS
Praesenzveranstaltung, Unterrichtssprache Englisch
Zeit und Ort: Di 8:15 - 9:45, HHP6 - R.EG.001; Fr 10:15 - 11:45, HHP6 - R.EG.001
vom 16.4.2024 bis zum 12.7.2024
- Studienfächer / Studienrichtungen
- PFL FinMath-MSc 2
- Voraussetzungen / Organisatorisches
- Basic knowledge of measure-theoretic probability. Knowledge of stochastic processes is not required, but helpful.
Modultitel:
Mathematical Finance
Modultitel:
Finanzmathematik und stochastische Integration
Modulhandbuch:
https://www.math.uni-kiel.de/de/studium_und_lehre/studienverlauf-module
Module alphabetisch:
http://www.math.uni-kiel.de/go/module
Modulcode: math-stifi:
https://www.math.uni-kiel.de/de/studium_und_lehre/studienverlauf-module/module/math-stifi.pdf
Zielgruppe:
1-Fach-Master Mathematik (Wahlbereich)
1-Fach-Master-Finanzmathematik (Pflicht)
Master Mathematics, Master Mathematical Finance
Link auf Internetseite:
https://lms.uni-kiel.de/url/RepositoryEntry/5434671277
- Inhalt
- When modeling random processes in time, one often encounters stochastic integrals - integrals whose integrand and integrator are stochastic processes. The resulting theory is rich and interesting from a mathematical point of view, but also plays an important role in many applications, for example in modern financial mathematics, but also in natural sciences and engineering. Stochastic calculus also plays a role in modern machine learning techniques such as stable diffusion.
The course is split in two parts:
1. Stochastic Calculus
2. Application to continuous time models for financial markets
It is possible to take only the first part of the course and complete it with a module examination.
Even if stochastic integrals appear again and again in a natural way, the stringent definition is not very easy and requires an expansion of the known notions of integrals. In this course we will also introduce the stochastic integral for jump processes, but then always work with continuous semimartingales to avoid technical problems. Based on this definition, we develop a calculus, the Itô calculus, which enables easy handling of stochastic integrals. At the end of the first part of the course, we will deal with internal and external mathematical applications of the previously developed theory.
The second part of the course deals with financial markets from a mathematical point of view. In particular, the analysis and evaluation of financial derivatives in realistic models requires knowledge of stochastic integration in order to be able to formulate the basic terms at all. On this basis, however, a critical understanding of the theory and practice of the financial markets can be developed. In doing so, we develop an exciting interplay between very practical questions and deep-seated mathematics.
We are particularly concerned with the (arbitrage-free) valuation of options. As an application of the theory, we will examine financial market models of the Black-Scholes type in more detail, but not limit ourselves to this model, but also consider models with jumps and stochastic volatility models.
- Empfohlene Literatur
- A. Irle. Finanzmathematik. Teubner.
Weitere Literatur wird ggf. in den Lehrveranstaltungen bekanntgegeben.
- Zusätzliche Informationen
- Erwartete Teilnehmerzahl: 15
- Zugeordnete Lehrveranstaltungen
- UE: Übung zu Finanzmathematik und Stochastische Integration
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Dozent/in: Prof. Dr. Sören Christensen
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