## OVERVIEW

*The aim of the course is to provide the student with the knowledge of advanced mathematical methods to successfully deal with economic models from a quantitative viewpoint.*

## AIMS AND CONTENT

LEARNING OUTCOMES

The course will provide the mathematical tools for the definition and the solution of dynamic optimization problems with particular emphasis to economic/financial models. Moreover, it will provide topics of probability theory in view of applications to choices in a risky framework.

AIMS AND LEARNING OUTCOMES

*At the end of the course, the student will be able to deal, autonomously and properly, with the learned mathematical topics and apply them to economic problems with the needed methodological rigor.*

PREREQUISITES

*The contents of the course of **Mathematics for Economics and Data Science**s I.*

TEACHING METHODS

*The course will be taught by frontal lectures. During the a.y. 2021/22 the lectures might be in blended mode.*

SYLLABUS/CONTENT

*Probability theory in discrete sample spaces: probability spaces; random variables; distribution and joint distribution of random variables; conditional probability and conditional distribution; expected value and conditional expected value; introduction to the theory of stochastic processes and martingales; application: overview on arbitrage theory in discrete time.*

*Dynamic optimization: formulation of optimal control problems; dynamic programming principle, HJB equations and verification theorem; application to economic models.*

RECOMMENDED READING/BIBLIOGRAPHY

Notes of the teacher. Further bibliographic material will be provided at the beginning of the course

## TEACHERS AND EXAM BOARD

**Office hours:** Office hours: Tuesday 10-30 - 12.30 on Teams

## LESSONS

TEACHING METHODS

*The course will be taught by frontal lectures. During the a.y. 2021/22 the lectures might be in blended mode.*

LESSONS START

February 2022

Class schedule

All class schedules are posted on the EasyAcademy portal.

## EXAMS

EXAM DESCRIPTION

*The exam will be written and will contain questions on the the theoretical and modeling features treated in the course as well as exercises.*

ASSESSMENT METHODS

*The exam will be in written test composed by theoretical questions and exercises. It will evaluate the understanding of the contents of the course with the goal of assessing the reached skill of applying the tools and the methods learned in an economic perspective and the specialistic language.*

*At the end of the course the teacher will privide some sample tests and will illustrate the evaluation procedure*

FURTHER INFORMATION

*Other information will be provided during the course. For non-attending students the same rules apply. *