Jarrow-Yildirim model for inflation: theory and applications

This thesis deals with inflation theory, focussing on the model of Jarrow & Yildirim, which is nowadays used when pricing inflation derivatives. After recalling main results about short and forward interest rate models, the dynamics of the main components of the market are derived. Then the most important inflation-indexed derivatives are explained (zero coupon swap, year-on-year, cap and floor), and their pricing proceeding is shown step by step. Calibration is explained and performed with a common method and an heuristic and non standard one. The model is enriched with credit risk, too, which allows to take into account the possibility of bankrupt of the counterparty of a contract. In this context, the general method of pricing is derived, with the introduction of defaultable zero-coupon bonds, and the Monte Carlo method is treated in detailed and used to price a concrete example of contract. Appendixes: A: martingale measures, Girsanov's theorem and the change of numeraire. B: some aspects of the theory of Stochastic Differential Equations; in particular, the solution for linear EDSs, and the Feynman-Kac Theorem, which shows the connection between EDSs and Partial Differential Equations. C: some useful results about normal distribution.

A ROS-based Workspace Control and Trajectory Planner for a seven degrees of freedom Robotic arm

In this Bachelor Thesis I want to provide readers with tools and scripts for the control of a 7DOF manipulator, backed up by some theory of Robotics and Computer Science, in order to better contextualize the work done. In practice, we will see most common software, and developing environments, used to cope with our task: these include ROS, along with visual simulation by VREP and RVIZ, and an almost "stand-alone" ROS extension called MoveIt!, a very complete programming interface for trajectory planning and obstacle avoidance. As we will better appreciate and understand in the introduction chapter, the capability of detecting collision objects through a camera sensor, and re-plan to the desired end-effector pose, are not enough. In fact, this work is implemented in a more complex system, where recognition of particular objects is needed. Through a package of ROS and customized scripts, a detailed procedure will be provided on how to distinguish a particular object, retrieve its reference frame with respect to a known one, and then allow navigation to that target. Together with technical details, the aim is also to report working scripts and a specific appendix (A) you can refer to, if desiring to put things together.