Prof. i. R. Dr. rer. nat. Hans Föllmer

• DFG-Forschungszentrum "Mathematik für Schlüsseltechnologien - MATHEON": Probabilistic interaction models for the microstructure of asset price fluctuation (Teilprojekt E 3)

  Quelle ↗

  In the standard economic paradigm, asset prices are determined by the markets view of their fundamental values. But there is usually no rigorous modeling of the interactions which lead to such an aggregate assessment. In the standard models of Mathematical Finance, the fluctuation of asset prices is simply given as a stochastic process, and the analysis of hedging and investment strategies starts from there. There is, however, an increasing awareness that this approach fails to capture some crucial sources of financial risk. One such source is the impact of interactive shifts in investor sentiment on asset prices which may generate a considerable liquidity risk. In order to analyze such effects in a more rigorous manner, one needs mathematical models for the microstructure of financial markets.

• DFG-Forschungszentrum "Mathematik für Schlüsseltechnologien - MATHEON": Beyond Value at Risk - Quantifying and Hedging the Downside Risk (Projekt E 4)

  Quelle ↗

  Hedging financial risk has become a major topic in academia as well as in the financial industry. In the context of the mathematical theory of incomplete financial markets, the key idea is to find a dynamic investment strategy which is optimal in terms of some criterion of risk-minimization. For criteria in terms of quadratic measures of risk, this problem has been investigated in depth and Berlin has played a leading role in this development. Recently, there is a growing emphasis on quantitative measures of the downside risk which reflect the concerns of a supervising agency. Such a measure of risk should determine the minimal capital requirement which, if added to a given financial position, makes the position acceptable from the point of view of risk management. "Value at Risk", the current industry standard, has serious deficiencies, both on the practical and on the theoretical level. In particular, it does not satisfy some natural requirements of consistency. This has triggered a systematic investigation of the general structure of reasonable measures of risk, leading to the notions of coherent risk measures and of convex risk measures.

Noch keine Publikationen aus OpenAlex zugeordnet.