Dozent:

M.Sc. Brice Hakwa

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Vorlesung:

Beginn der Vorlesung: 09.04. bis 12.07.2012
Mo. 16:00 - 18:00 G.15.25 / wöchentlich
Do. 14:00 - 16:00 G.16.09 / wöchentlich

Ausfalltermin:

keine

Inhaltsverzeichnis

1. Motivation
2. Element of Probability Theory
1. Probability Space
2. Random Variable
3. Distribution and density Function
4. Characteristic function
5. Moment of random variable
6. Transformation Formula and Somme of Random Variables
7. Infinitely divisible and Stable Distribution
8. Type of Convergence for random Variables
9. Conditional expectation
3. Generalities of stochastic processes
1. Definition and Classification
1. Definition
2. Measurability and filtration
3. Variation of a Process
4. Moments, Covariance and Increment of a Process
5. Equivalence of Processes^
2. Martingale
3. Stopping times
4. Markov Property
1. Generalities
2. Discrete Time Markov Chain
3. Limiting and Stationary Distribution
4. Continuous time Markov Process
4. Stochastic Process in Finance
1. Brownian motion
2. Processes derived from the BM.
1. Brownian Bridge BB.pdf
2. BM. With Drift
3. Geometric BM gbm.pdf
3. Counting and marked processes
4. Poisson process Poisson.pdf
5. Compound Poisson process Anwendungsbeispiel
6. Compensated Poisson processes
5. Stochastic calculus with respect to the BM.
1. Wiener stochastic integral
2. Stochastic integral of simple function
3. Ito stochastic integral
4. Stochastic differential equation
5. Diffusion process
1. Existence and uniqueness
2. Markov property
3. Infinitesimal generator
4. Dynkin's formula and Martingale
6. Simulation methods for SDE Link:Zusatzliteratur.pdf
6. Monte-Carlo-Simulation.pdf
7. Introduction to Levy process Link: Zusatzliteratur.pdf
1. Definition
2. Markov property of levy processes
3. Jump measure and Levy measure
4. Mean and variance of levy process
5. Pathwise properties of levy process

Litteratur:

• Steven E. Shreve, Stochastic Calculus for Finance II, Continuous-Time Models
• Bernt Øksendal, Stochastic Differential Equations: An Introduction with Applications
• Ken-Iti Sato, Levy Processes and Infinitely Divisible Distribution
• Erhan Cinlar, Probability and Stochastics
• Rama Cont, financial modelling with jump processes
• Nicholas H. Bingham Rüdiger Kiesel, Risk-Neutral Valuation

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Übung:

Beginn: 04.04.12 - 11.07.2012
Mi. 14:00 - 16:00 D.13.08 / wöchentlich

Übungsleiter:

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Voraussetzungen

Master an Universitäten - Mathematik