• Convex Risk Measure
• Delta Hedging
• Financial mathematics.
• Option
• Recursive Neural Network

In this work we apply Recursive Neural Networks in finance, namely we use Recursive Neural Networks to compute the Delta Hedging of Options, in particular Vanilla Options.\\
In the first part of this work, we will introduce the procedure of Delta Hedging and define the concepts of Pricing and of Convex Risk Measures, it is preparatory for the third chapter.
In the second chapter, we will introduce the concept of Neural Network and prove a version of the theorem of Universal Approximation for Neural Networks.
The third chapter is the main chapter of this work, we compare the results of hedging with a Neural Network and Hedging with the classical model for simulations created with the model of Black and Scholes and the Heston model, following the article Deep Hedging (arXiv:1802.03042). Subsequently, we expand what it is done in the article by comparing the results of these two techniques in the case of the Model with a different regularity, the model of Black and Scholes with Jumps. We will see that the Neural Network is able to give results comparable with the one of the classical financial theory in all of these cases.