Search result: Catalogue data in Autumn Semester 2020
|Computational Science and Engineering Bachelor|
|For All Programme Regulations|
|Fields of Specialization|
|401-3913-01L||Mathematical Foundations for Finance||W||4 credits||3V + 2U||M. Schweizer|
|Abstract||First introduction to main modelling ideas and mathematical tools from mathematical finance|
|Objective||This course gives a first introduction to the main modelling ideas and mathematical tools from mathematical finance. It aims mainly at non-mathematicians who need an introduction to the main tools from stochastics used in mathematical finance. However, mathematicians who want to learn some basic modelling ideas and concepts for quantitative finance (before continuing with a more advanced course) may also find this of interest. The main emphasis will be on ideas, but important results will be given with (sometimes partial) proofs.|
|Content||Topics to be covered include|
- financial market models in finite discrete time
- absence of arbitrage and martingale measures
- valuation and hedging in complete markets
- basics about Brownian motion
- stochastic integration
- stochastic calculus: Itô's formula, Girsanov transformation, Itô's representation theorem
- Black-Scholes formula
|Lecture notes||Lecture notes will be made available at the beginning of the course.|
|Literature||Lecture notes will be made available at the beginning of the course. Additional (background) references are given there.|
|Prerequisites / Notice||Prerequisites: Results and facts from probability theory as in the book "Probability Essentials" by J. Jacod and P. Protter will be used freely. Especially participants without a direct mathematics background are strongly advised to familiarise themselves with those tools before (or very quickly during) the course. (A possible alternative to the above English textbook are the (German) lecture notes for the standard course "Wahrscheinlichkeitstheorie".)|
For those who are not sure about their background, we suggest to look at the exercises in Chapters 8, 9, 22-25, 28 of the Jacod/Protter book. If these pose problems, you will have a hard time during the course. So be prepared.
|401-4657-00L||Numerical Analysis of Stochastic Ordinary Differential Equations |
Alternative course title: "Computational Methods for Quantitative Finance: Monte Carlo and Sampling Methods"
|W||6 credits||3V + 1U||D. Salimova|
|Abstract||Course on numerical approximations of stochastic ordinary differential equations driven by Wiener processes. These equations have several applications, for example in financial option valuation. This course also contains an introduction to random number generation and Monte Carlo methods for random variables.|
|Objective||The aim of this course is to enable the students to carry out simulations and their mathematical convergence analysis for stochastic models originating from applications such as mathematical finance. For this the course teaches a decent knowledge of the different numerical methods, their underlying ideas, convergence properties and implementation issues.|
|Content||Generation of random numbers|
Monte Carlo methods for the numerical integration of random variables
Stochastic processes and Brownian motion
Stochastic ordinary differential equations (SODEs)
Numerical approximations of SODEs
Applications to computational finance: Option valuation
|Lecture notes||There will be English, typed lecture notes for registered participants in the course.|
|Literature||P. Glassermann: |
Monte Carlo Methods in Financial Engineering.
Springer-Verlag, New York, 2004.
P. E. Kloeden and E. Platen:
Numerical Solution of Stochastic Differential Equations.
Springer-Verlag, Berlin, 1992.
|Prerequisites / Notice||Prerequisites:|
Mandatory: Probability and measure theory,
basic numerical analysis and
basics of MATLAB programming.
a) mandatory courses:
Probability Theory I.
b) recommended courses:
Start of lectures: Wednesday, September 16, 2020.
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