## Courses

##### Last Updated:

All Courses @ IAM Actuarial Science Cryptography Financial Mathematics Scientific Computing

### Selected Courses for Financial Mathematics

**Credit: **
3(3-0); **ECTS: **
8.0

See the course in IAM Catalogue or METU Catalogue

**Credit: **
0(0-0); **ECTS: **
50.0

See the course in IAM Catalogue or METU Catalogue

**Credit: **
3(3-0); **ECTS: **
8.0

See the course in IAM Catalogue or METU Catalogue

**Credit: **
3(3-0); **ECTS: **
8.0

See the course in IAM Catalogue or METU Catalogue

**Credit: **
3(3-0); **ECTS: **
8.0

See the course in IAM Catalogue or METU Catalogue

**Credit: **
3(3-0); **ECTS: **
8.0

See the course in IAM Catalogue or METU Catalogue

**Credit: **
3(3-0); **ECTS: **
8.0

See the course in IAM Catalogue or METU Catalogue

**Credit: **
3(3-0); **ECTS: **
8.0

See the course in IAM Catalogue or METU Catalogue

**Credit: **
3(3-0); **ECTS: **
8.0

See the course in IAM Catalogue or METU Catalogue

**Credit: **
3(3-0); **ECTS: **
8.0

See the course in IAM Catalogue or METU Catalogue

**Credit: **
3(3-0); **ECTS: **
8.0

See the course in IAM Catalogue or METU Catalogue

**Credit: **
3(3-0); **ECTS: **
8.0

Part I: Probability spaces, random variables, probability distributions and probability densities, conditional probability, Bayes formula, mathematical expectation, moments. Part II: Sampling distributions, decision theory, estimation (theory and applications), hypothesis testing (theory and applications), regression and correlation, analysis of variance, non-parametric tests.

See the course in IAM Catalogue or METU Catalogue

**Credit: **
3(3-0); **ECTS: **
8.0

See the course in IAM Catalogue or METU Catalogue

**Credit: **
3(3-0); **ECTS: **
8.0

See the course in IAM Catalogue or METU Catalogue

**Credit: **
3(3-0); **ECTS: **
8.0

See the course in IAM Catalogue or METU Catalogue

**Credit: **
3(3-0); **ECTS: **
8.0

See the course in IAM Catalogue or METU Catalogue

**Credit: **
3(3-0); **ECTS: **
8.0

See the course in IAM Catalogue or METU Catalogue

**Credit: **
3(3-0); **ECTS: **
8.0

See the course in IAM Catalogue or METU Catalogue

**Credit: **
3(3-0); **ECTS: **
8.0

See the course in IAM Catalogue or METU Catalogue

**Credit: **
3(3-0); **ECTS: **
8.0

See the course in IAM Catalogue or METU Catalogue

**Credit: **
3(3-0); **ECTS: **
8.0

See the course in IAM Catalogue or METU Catalogue

**Credit: **
3(3-0); **ECTS: **
8.0

See the course in IAM Catalogue or METU Catalogue

**Credit: **
2(2-0); **ECTS: **
6.0

LaTeX and Matlab; Basic Commands and Syntax of LaTeX and Matlab; Working within a Research Group via Subversion; Arrays and Matrices; Scripts and Function in Matlab; Commands and Environments in LaTeX; More on Matlab Functions; Toolboxes of Matlab; Packages in LaTeX; Graphics in Matlab; Handling Graphics and Plotting in LaTeX; Advanced Techniques in Matlab: memory allocation, vectoristaion, object orientation, scoping, structures, strings, file streams.

See the course in IAM Catalogue or METU Catalogue

**Credit: **
2(2-0); **ECTS: **
6.0

Review of Programming and Toolboxes, Packages, Modules; Iterative Linear Algebra Problems; Root Finding Programs; Recursive Functions and Algorithms; Optimisation Algorithms; Data Fitting and Interpolation; Extrapolation; Numerical Integration; Numerical Solutions of Differential Equations: IVPs and BVPs; Selected Topics (algorithms and coding in different fields).

See the course in IAM Catalogue or METU Catalogue

**Credit: **
0(0-0); **ECTS: **
130.0

See the course in IAM Catalogue or METU Catalogue

**Credit: **
3(3-0); **ECTS: **
8.0

See the course in IAM Catalogue or METU Catalogue

**Credit: **
3(3-0); **ECTS: **
8.0

See the course in IAM Catalogue or METU Catalogue

**Credit: **
3(3-0); **ECTS: **
8.0

See the course in IAM Catalogue or METU Catalogue

**Credit: **
3(3-0); **ECTS: **
8.0

**Numerical Methods for Discrete Time Models:**binomial method for options; discrete time optimal control problems.

**Reminders on Continuous Models:**Ito process and its applications in stock market, Black-Scholes equation and its solution; Hedging, Volatility smile.

**Monte Carlo Method for Options:**generating random numbers, transformation of random variables and generating normal variates; Monte Carlo integration; pricing by Monte Carlo integration; variance reduction techniques, quasi-random numbers and quasi-Monte Carlo method.

**Finite Difference Methods for Options:**explicit and implicit finite difference schemes, Crank-Nicolson method; Free-Boundary Problems for American options.

**Finite Difference Methods for Control Problems:**Markov Chain approximation method, elliptic Hamiltion-Jacobi-Bellman equations, computational methods.

See the course in IAM Catalogue or METU Catalogue

**Credit: **
3(3-0); **ECTS: **
8.0

See the course in IAM Catalogue or METU Catalogue

**Credit: **
3(3-0); **ECTS: **
8.0

See the course in IAM Catalogue or METU Catalogue

**Credit: **
3(3-0); **ECTS: **
8.0

See the course in IAM Catalogue or METU Catalogue

**Credit: **
3(3-0); **ECTS: **
8.0

Important markets such as commodities or credit derivatives are essentially incomplete. The recent financial crisis has increased even more the importance of pricing and hedging in incomplete markets. Therefore these lectures concentrate on advanced methods of stochastic finance required in the context of incomplete markets. We will consider both, process in discrete and continuous time.

The content of the course covers in particular the following topics: market efficiency, market incompleteness; perfect hedges; equivalent martingale measures; attainable payoffs; asset management; contingent claims; replicating portfolio; dynamical arbitrage theory; arbitrage-free pricing; geometric characterization of arbitrage; von Neumann representation; robust Savage representation; expected utility; fair value; certainty equivalent; risk premium; risk aversion; equilibrium pricing; relative entropy; convex risk measures; robust representation; coherent risk measures; VAR; average VAR; upper/lower hedging prices; superhedging duality; risk indifference pricing; HJB equations; dynamical programming.

See the course in IAM Catalogue or METU Catalogue

**Credit: **
3(3-0); **ECTS: **
8.0

See the course in IAM Catalogue or METU Catalogue

**Credit: **
3(3-0); **ECTS: **
8.0

See the course in IAM Catalogue or METU Catalogue

**Credit: **
3(3-0); **ECTS: **
8.0

See the course in IAM Catalogue or METU Catalogue

**Credit: **
3(2-2); **ECTS: **
8.0

See the course in IAM Catalogue or METU Catalogue

**Credit: **
3(3-0); **ECTS: **
8.0

See the course in IAM Catalogue or METU Catalogue

**Credit: **
3(3-0); **ECTS: **
8.0

This course is an introduction to the mathematical formulation and treatment of problems arising from trade execution in financial markets. When there are costs and constraints imposed on the execution of trades, how to best execute them? The course studies mathematical formulations and solutions of these types of problems.

See the course in IAM Catalogue or METU Catalogue

**Credit: **
3(3-0); **ECTS: **
8.0

See the course in IAM Catalogue or METU Catalogue

**Credit: **
3(3-0); **ECTS: **
8.0

See the course in IAM Catalogue or METU Catalogue

**Credit: **
3(3-0); **ECTS: **
8.0

See the course in IAM Catalogue or METU Catalogue

**Credit: **
3(3-0); **ECTS: **
8.0

Generating Random Numbers; Basic Principles of Monte Carlo; Numerical Schemes for Stochastic Differential Equations; Simulating Financial Models; Jump-Diffusion and Levy Type Models; Simulating Actuarial Models; Markov Chain Monte Carlo Methods.

See the course in IAM Catalogue or METU Catalogue

**Credit: **
3(3-0); **ECTS: **
8.0

Convexity; Gradient Descent; Stochastic Gradient Methods; Noise Reduction Methods; Second-Order Methods; Adaptive Methods; Methods for Regularized Models; Introduction to Machine Learning: support machine vector, neural network.

See the course in IAM Catalogue or METU Catalogue

**Credit: **
3(0-0); **ECTS: **
8.0

See the course in IAM Catalogue or METU Catalogue

**Credit: **
3(3-0); **ECTS: **
8.0

See the course in IAM Catalogue or METU Catalogue

**Credit: **
3(0-0); **ECTS: **
8.0

See the course in IAM Catalogue or METU Catalogue

**Credit: **
3(3-0); **ECTS: **
8.0

See the course in IAM Catalogue or METU Catalogue