From a mathematical point-of-view, we will first introduce point processes and then Hawkes processes. We will show that the self-exciting structure of Hawkes

*Mini course announcement* Prof. Simone Mattia Scotti [ LPMA, Université Paris Diderot ] will give a mini course on *Real markets, microstructure, clusters and Hawkes with a Branching process point of view*, according with the following time table: 21st of March (2017) : Room I 1430-1730 23rd of March (2017) : Room M 1530-1730 24th of March (2017) : Room M 1430-1730 all the lessons will take place at the Dept. of Computer Science - UniVr Strada le Grazie, 15 - Verona Ca' Vignal located here https://goo.gl/maps/Yx2JU *Abstract and structure of the course* The analysis of real financial markets, along with the study of related economic time series, represents an increasing field of research and development of effective applications, from the stochastic processes point of views, as well as from the statistic and computational sides of the moon. In this mini-course, we first recall the classical framework behind the modern and mathematically rigorous, theory of finance, starting from the treatment of continuous-path stochastic processes. Then, we focus on the microstructure of market data, discussing both limit and market orders, along with correlated liquidity problems. In a second part, we will specialize our analysis on a particular feature of financial markets, namely the existence of jumps' cluster. It is worth to mention that the latter has been highlighted in recent literature in microstructure, showing to have a deep impact on real markets and representing a main research axis in the field. processes can easily explain some features exhibited by financial data, e.g. the cluster effects. In the third part, we will introduce the branching processes (CBI) showing that they can be seen as a natural extension (marked versions) of Hawkes processes. We will show that this class of models has very nice properties from computational as well as from analytical point of view, particularly by exploiting the Dawson-Li representation. Moreover, we will point out some unexpected features of the aforementioned approaches, such, e.g., the persistency of low interest rates and negative risk premium in electricity markets. A detailed bibliograpy will be given during the course. ___________ Do not hesitate to contact me for further details: luca.dipersio@univr.it LuCa -- __ Luca Di Persio - PhD assistant professor of Probability and Mathematical Finance Dept. Informatics University of Verona strada le Grazie 15 - 37134 Verona - Italy Tel : +39 045 802 7968 <+39%20045%20802%207968> Dept. Math University of Trento V. Sommarive, 14 - 38123 Povo - Italy Tel : +39 0461 281686 <+39%200461%20281686>