Economics

The course aims at enabling students to grasp the basic mathematical topics and tools needed in Economics and Firm Management modelling, such as linear algebra, multivariable functions, static optimization methods, and techniques to solve differential equations. Students that pass the exam will be able to handle quadratic forms, to study their sign, to diagonalize matrices, to work with multivariable functions, such as utility and production functions, to optimize functionals depending on them, with or without constraints, to calculate Lagrange multipliers, and to solve differential equations. The course requires a good knowledge of basic mathematics and financial mathematics acquired in three-year degree courses; it is closely related to the course of Probability and Stochastic Processes and provides the basis for the subsequent teachings of Risk Theory, Quantitative finance, Methods and models for finance, Times series, Actuarial mathematics for the private companies of the same course graduation. Knowledge and understanding: After attending the course, students will be able to know the evaluation procedures of financial problems and to understand the results of mathematical models used to resolve those problems. Ability to apply knowledge and comprehension: At the end of the course, students will be able to use basic mathematical tools to evaluate financial problems in accordance with any robust financial theory and to apply a right knowledge in their use to real evaluation problems. Judgment skills: At the end of the course students will be able to understand the results derived from the financial tools applied and to explain differences among figures obtained from different models, in relation to the theoretical setting in wich the evaluation is provided. Communication skills: After passing the exam, students will be able to explain and discuss about the arguments treated during the course, giving their comments and remarks on the use of the mathematical tools learnt. Self-learning skills: After passing the exam, students will have a knowledge of the advanced mathematical topics and tools for financial modelling that will permit them to face future studies in mathematical finance for pricing of liquid and illiquid financial instruments.