Π.Μ.Σ στη «Χρηματοοικονομική και Τραπεζική»

## Quantitative Methods-Statistics

Full Time// Preaparatory

Part Time // Preaparatory

## Learning Outcomes

The first part Quantitative Methods, presents the basic tools and methods of mathematics which are extensively found throughout the range of financial theory and analysis. The course aims to stimulate the study of the associated mathematical techniques through analytical problems in the economy, and then employ them in appropriate economic models. Linking techniques with their applications, it establishes the inextricable relationship between quantitative methods and economic theory.

Upon successful completion of the course, the students will be able to

• perform operations with matrices.
• interpret graphically operations with vectors.
• compute the determinant and the inverse of a matrix.
• solve linear systems via the method of the inverse matrix and the method of Cramer.
• compute, graphically and algebraically, limits of functions.
• interpret and apply, graphically and algebraically, the notion of continuity.
• interpret graphically and compute algebraically the derivative of a function.
• compute the monotonicity, the convexity, and the extreme points of one-variable functions via the 1st and 2nd order conditions.
• compute the extreme points of multi-variable functions via the generalized 1st and 2nd order conditions.
• compute the extreme points of multi-variable functions subject to equations as constraints, according to the method of the Lagrange multiplier.
• compute indefinite integrals via elementary methods, such as integration-by-parts and change-of-variable.
• interpret and compute the definite integral of a function, as well as to apply it for finding areas of sectors.

The second part is an introduction to Descriptive Statistics and Probability Theory. The purpose of the course is to present the basic tools of these two branches of Statistics, widely applied in Economics and Finance. Knowing these techniques of Statistical Analysis is a key skill that allows us to quantify real economic and financial problems, explore the available data, and arrive at logical conclusions and forecasts. Upon successful completion of the course, the student will be able to have: 1) An understanding of the basic concepts of Descriptive Statistics and Probability Theory. 2) Knowledge of the basic tools and techniques of Descriptive Statistics and Probability Theory. 3) Use Descriptive Statistics and Probability Theory methodologies in Financial Studies

## General Competences

• Decision-making.
• Individual/Independent work.
• Critical thinking.
• Development of free, creative and inductive thinking.

## Course Content

The following sections will be presented:

• Static Analysis: Equilibrium Analysis – The Linear Model – Matrix Algebra – Determinants – Linear Systems
• Comparative Static Analysis: Derivatives – Limits – Continuity – Differentiation Rules – Applications to Revenue and Cost Functions –   Inverse Function – Partial Derivatives – Applications to the Linear Model
• Optimization Problems: Optimization of a One-Variable Function – Optimization of a Multi-Variable Function –  Optimization of a Function with Equations as Constraints – Utility Maximization
• Dynamic Analysis: Economic Dynamics – Indefinite Integrals – Integration Rules – Definite Integrals – Generalized Integrals – Present Value of Money Flow – Domar’s Growth Model – 1st Order Differential Equations with Constant Coefficients – The Dynamics of Market Price

Data description, samples and statistical variables, presentation of statistical data, population parameters, empirical distributions. Probability space, events and probabilities, conditional probabilities. Continuous and discrete random variables. Cumulative distribution functions, probability distribution functions, probability density functions, definitions and properties. Moments of random variables. The joint distribution of random variables. Covariance and its properties. Marginal distributions. Independent random variables. Independence vs. linear independence. Correlation coefficient. Independence and tautonomy of random variables. The concept of random sample

## Student Performance Evaluation

The course is preparatory and does not include a student performance evaluation procedure.

## Bibliography

Suggested Bibliography

• Alpha C. Chiang – Kevin Wainwright, Μαθηματικές Μέθοδοι Οικονομικής Ανάλυσης – Νέα Αναθεωρημένη Έκδοση, Κριτική, 2011.
• Πέτρος Α. Κιόχος και Απόστολος Π. Κιόχος, Στατιστική για τις επιχειρήσεις και την οικονομία, Εκδόσεις Ελένη Κιόχου, Αθήνα 2015.
• Τάκης Παπαϊωάννου, Εισαγωγή στις Πιθανότητες, Εκδόσεις Σταμούλη, 2000.