大阪大学　数理・データ科学教育研究センター
Center for Mathematical Modeling and Data Science,Osaka University

Analyzing the fine structure of stochastic processes

Jeannette Woerner (Professor, Technical University of Dortmund)

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4. Analyzing the fine structure of stochastic processes

大阪大学 金融・保険セミナーシリーズ 第21回

Analyzing the fine structure of stochastic processes

Jeannette Woerner (Professor, Technical University of Dortmund)

In the recent years starting from the Black-Scholes model in mathematical finance many different models either based on semimartingales, purely continuous, pure jump and a mixture of both, or fractional Brownian motion have been proposed in an attempt to capture the empirical facts of real data both in finance and physics, e.g. heavy tails, skewness, excess kurtosis and long range dependence.

We propose to include the fine structure into this analysis, which makes it possible to distinguish between semimartingales and fractional Brownian motion on the one hand and on the other hand determine the presence of jumps and measurement errors or market microstructure.

We will compare two different approaches, one based on the regularity of the sample paths, the other one based on the correlation structure.
For both methods we provide consistency and a distributional theory
and apply them to high frequency financial data and turbulence data.
Furthermore, the distributional theory for fractional Brownian motion based models provides some new insight in the scaling laws
for turbulence data.