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Statistical Inference and Malliavin Calculus

Final Report Summary - STATINF (Statistical Inference and Malliavin Calculus)

The researcher has achieved with success all the objectives of the project. On one hand, the researcher has solved problems of statistical inference for stochastic differential equations (sdes), which was the first goal of the project. More concretely, in this topic, the researcher has published five papers, submitted one, and has two in preparation. In two of the papers, the researcher has studied sdes with jumps, very important when modeling financial log prices, and has organized a first workshop on the topic in the host institution, where the both papers were presented. Another paper is focused on sdes driven by fractional Brownian motion, which are extensively used for modeling time evolution of phenomena in many scientific areas. In order to promote the transfer of knowledge of this topic to the members of the host institution and abroad, the researcher has organized in collaboration with E. Alòs -an expert in the topic from the host institution- another workshop where top researchers working in rough models and applications were invited. Last but not least, two papers deal with stochastic partial differential equations, they were not in the first objectives of the project but appeared after discussions with some professors invited to the statistics seminar of the host institution.

In the second period of the project, the researcher has been focused in developing the most applied part, which has been essential for the career development of the researcher in the host institution since it is an Economics Department. Moreover, these recent applied findings will attract a wide class of researchers and also non-scientific public. Specifically, four papers are completed, all dealing with simulated data and two including real data. The first paper is accepted in the Journal of Computational Finance, and improves the numerical computations of some financial values called greeks, used a lot by banks and financial institutions. The other three papers are submitted and are written in collaboration with C. Brownlees from the host institution. In those papers, a new way of representing the dependence structure of multidimensional models as a network is introduced. This network structure can also be used in problems of data science in order to deal with big data problems. In the host institution, a new Data Science Center has been built, and the researcher expects to start new collaborations and promote new activities related to these problems. Furthermore, a second workshop based on this topic has been organized in the host institution, where the three papers have been presented.

All publications are accepted in worldwide journals of Probability, Statistics, Econometrics and Finance, that will contribute to the excellence of the host institution as well as the European research area. The researcher has acquired a research network of connections with first class researchers in Probability and Statistics while working with her collaborators from France, Spain, Switzerland, Japan, UK and USA, which has been strengthen while starting the new collaborations with researchers of the host institution, that will also benefit from this network that she has created. In the host institution, the researcher has supervised 1 PhD student, is collaborating with a second one, and has supervised several Master projects from the Master in Finance. This will contribute to create a new generation of capable researchers with strong training in Probability, Statistics and Finance.

The researcher has been invited to several international conferences to present all these results. After finishing the two papers in preparation, the researcher expects to start new collaborations with the members of the host institution that have showed a lot of interest in the three organized workshops and papers achieved. She also expects to supervise new PhD students. For this, she has introduced some of the recent finding in her course of Pricing Financial Derivatives of the Master in Finance in the host institution, and also proposes related subjects to the final projects that she supervises, in order to find potential PhD students.

Website of the project: https://www.upf.edu/web/eulalia-nualart