Processi di branching e di Hawkes: teoria e applicazione al mercato dell'energia

In this work we want to study the structural properties of stochastic of Continuous state Branching process with Immigration (CBI) and Hawkes processes and we want to use them in financial applications to the commodities market and in particular Power market. The thesis is structured in three chapters: in the first one we review the definition and main properties of CBI and Hawkes properties, in the second one the first part is devoted to some important stochastic analysis results (Girsanov theorem) while in the second part we set up the SDE de-scribing the dynamic of an asset with jump part driven by an Hawkes process and by a CBI process and then we discuss about the procedure of switching to an equivalent arbitrage free probability measure, finally in the third chapter we present a model for power forward prices focusing our attention on a jump detection algorithm and using it to estimate jumps in historical series of future prices of other commodities (gold and crude oil).