About this Research Topic
In this Research Topic, we study long-memory models in mathematical finance. The classical models for financial time-series, especially those connected to pricing and hedging of financial derivatives, are Markovian or semimartingales. However, in recent 20 years it has been demonstrated that some financial time-series exhibit so-called long-range dependence. The future data is not statistically independent from the data from the distant past. This is in stark contrast of the Markovian assumption. Also, the long-range dependence does not fit naturally into the semimartingale setting. Therefore, new mathematical models are needed to capture the statistical nature of financial time-series. Furthermore, new mathematical theory is needed to analyze these models.
The aim of the Research Topic is to study existing long-range dependent models, such as the fractional Brownian motions and their generalizations, as well as to propose and study new long-range dependent models.
The scope of the Research Topic includes, but is not limited to:
1. The foundations of mathematical finance such as the theory of arbitrage and hedging and the implications of the existence of long-range dependence to the said foundations.
2. Mathematical foundations of long-range dependent stochastic processes including theories of stochastic integration, prediction and numerical methods.
3. Statistical analysis of long-range dependent models such as parameter estimation and calibration including implied volatility methods.
4. Simulation of long-range dependent models.
5. Empirical studies.
Keywords: mathematical finance, financial engineering, time-series analysis, long-range dependence, stochastic modeling
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