Main Application Area "Random phenomena in nature and economy"
Overview
Modern statistical and probabilistic methods form the theoretical basis to model and analyze complex stochastic phenomena. WIAS has, with main mathematical contributions, become an authority in this field including its applications to problems in science, technology, medicine and environmental research as well as risk evaluation for financial products.
Research on interacting random systems includes mathematical models for the description and understanding of physical phenomena and phase transitions like condensation effects in interacting particle systems, ageing of random trajectories in random media and solid-gas transitions in rigid bodies at positive low temperatures. Classical as well as quantummechanical many-particle systems are considered. Furthermore, coagulation processes (like growth of gas bubbles, soot-production, mergence of drops in clouds) are investigated with the help of systems of coupled stochastic differential equations. Further applications of probabilistic models deal with connectivity problems in mobile ad-hoc networks in telecommunication.
Research in statistics focuses on adaptive smoothing methods, the modeling and analysis of complex, usually high-dimensional data structures (dimension reduction) and the analysis of statistical inverse problems. Modern methods for risk assessment and evaluation in financial markets are developed using efficient stochastic algorithms that relay on methods for stopping and control problems in discrete and continuous time, analysis of advanced financial models and the analysis of stochastic differential equations. They form the basis of various applications in mathematical finance, such as pricing of American options, calibration of stock and interest rate models, and volatility estimation.
Research on interacting random systems includes mathematical models for the description and understanding of physical phenomena and phase transitions like condensation effects in interacting particle systems, ageing of random trajectories in random media and solid-gas transitions in rigid bodies at positive low temperatures. Classical as well as quantummechanical many-particle systems are considered. Furthermore, coagulation processes (like growth of gas bubbles, soot-production, mergence of drops in clouds) are investigated with the help of systems of coupled stochastic differential equations. Further applications of probabilistic models deal with connectivity problems in mobile ad-hoc networks in telecommunication.
Research in statistics focuses on adaptive smoothing methods, the modeling and analysis of complex, usually high-dimensional data structures (dimension reduction) and the analysis of statistical inverse problems. Modern methods for risk assessment and evaluation in financial markets are developed using efficient stochastic algorithms that relay on methods for stopping and control problems in discrete and continuous time, analysis of advanced financial models and the analysis of stochastic differential equations. They form the basis of various applications in mathematical finance, such as pricing of American options, calibration of stock and interest rate models, and volatility estimation.
Highlights
Within the DFG Research Center MATHEON two projects focus on applications in neuroscience (Project „A3 - Image and signal processing in medicine and biosciences”) and modeling and evaluation of financial products (Project „E5 - Statistical and numerical methods in modeling of financial derivatives and valuation of portfolio risk”).
Two other MATHEON-projects „B20 - Optimization of gas transport” and „C7 - Mean-risk optimization of electricity production in liberalized markets” deal with the application of stochastic optimization in energy production and distribution (electricity portfolio).
Several projects within the DFG Collaborative Research Center SFB 649 concentrate on the evaluation of economic risk.
In the frame of the DFG research unit FOR718, „Analysis and Stochastics in Complex Physical Systems” which is hosted at WIAS, research focuses on the interaction of probability theory with analysis and mathematical physics to rigorously understand the physics of the phase transition with the help of complex random interacting systems. There is a close partnership with probabilists from TU Berlin and with PhD students and postdocs from the IRTG „Stochastic Models of Complex Processes”. RTG 1845 „Stochastic Analysis with applications in biology, finance and physics”.
Two other MATHEON-projects „B20 - Optimization of gas transport” and „C7 - Mean-risk optimization of electricity production in liberalized markets” deal with the application of stochastic optimization in energy production and distribution (electricity portfolio).
Several projects within the DFG Collaborative Research Center SFB 649 concentrate on the evaluation of economic risk.
In the frame of the DFG research unit FOR718, „Analysis and Stochastics in Complex Physical Systems” which is hosted at WIAS, research focuses on the interaction of probability theory with analysis and mathematical physics to rigorously understand the physics of the phase transition with the help of complex random interacting systems. There is a close partnership with probabilists from TU Berlin and with PhD students and postdocs from the IRTG „Stochastic Models of Complex Processes”. RTG 1845 „Stochastic Analysis with applications in biology, finance and physics”.
Contributing groups: