Stochastic Algorithms and Nonparametric Statistics

The group contributes to the following application oriented research topics of WIAS:

Calibration of realistic stock and interest rate models is of prime importance. While standard interest rate products such as caps and swaptions can be priced (quasi-) analytically in a single curve Libor market model, it is impossible to match cap and swaption volatility smiles and skews observed in the markets using this model. Moreover, after the financial crisis the Libor rate could not be considered risk free anymore. [>> more]

Image processing tools based on mathematical algorithms from statistics or variational methods enable a bulk of applications in the medical sciences. They range from image enhancement to automatic image analysis. In many cases, a significant improvement in the results results of image analysis can be achieved by integrating the physics of the imaging process. Applications of these methods range from tomography images to various modalities of magnetic resonance imaging. [>> more]

Optimization problems in energy management are concerned with the planning of production and distribution of different energy sources (power, gas), in order to cover a given customer's demand. In this context, the consideration of uncertainties (e.g., loads, meteorological parmeters, prices) in transportation networks represents a major challenge. The aim is to find cost optimal decisions which are robust at the same time with respect to uncertainties. The additional consideration of markets and the physica of energy transport then lead to risk-averse optimal control problems with equilibrium constraints. [>> more]

Derivatives of complex structured financial instruments with early exercise features (e.g. American style products and energy swing options) are important instruments traded at financial and energy markets. Such products give the holder the right to exercise a cash-flow or energy unit or a stream of cash-flows (energy units) at any date before expiry. For example, an investor may buy an option to swap his floating interest rates or electricity payments for example with fixed rate payments specified in the contract. Particularly for new applications in energy markets, these solutions are extended for solving problems of optimal control. [>> more]

Archive

Further application topics where the institute has expertise in:

Dynamic process simulation has become an indispensable tool for design, analysis, and operation of complex plants in industry. Here initial value problems for large systems of differential-algebraic equations (DAEs) have to be solved. The simulation concept developed at WIAS exploits the modular structure of the process models to use divide-and-conquer techniques for solving the DAE system with block-structured methods. The concept is implemented in the Simulator BOP and has been successfully used in different industrial applications. [>> more]

The valuation and risk assessment of financial products requires appropriate analysis of the characteristics involved in the modeling. Particular examples are volatility and characteristics of extreme events. Usually the models under consideration are multi-dimensional and have time dependent parameters. [>> more]