60
Mathematics for Economics, Actuarial Studies and Finance
REGGIO DI CALABRIA
Overview
Date/time interval
Syllabus
Course Objectives
The course "Quantitative Methods for Economics and Finance" provides comprehensive training in mathematical and statistical tools for economic and financial analysis.
Learning Objectives:
1. Core Competencies
- Master financial mathematics and time value of money concepts
- Apply investment appraisal techniques for capital budgeting decisions
- Understand and manage uncertainty and risk in financial decision-making
2. Portfolio Management Skills
- Optimize investment portfolios using mean-variance analysis
- Quantify risk-return trade-offs effectively
- Implement diversification strategies based on correlation analysis
3. Market Models Knowledge
- Apply CAPM and multi-factor models for cost of capital determination
- Analyze systematic risk components and factor sensitivities
- Understand market equilibrium dynamics and pricing relationships
4. Practical Skills
- Implement theoretical models using computational tools
- Estimate parameters from historical data while managing statistical uncertainty
- Conduct sensitivity analysis and model validation
Expected Learning Outcomes:
Upon completion of the course, students will be able to evaluate complex investment projects, construct optimal portfolios, apply equilibrium models for risk pricing, and use advanced quantitative methodologies to support economic and financial decision-making in professional contexts.
The course combines theoretical rigor with practical applications, preparing students to tackle quantitative challenges in economics and finance with confidence and competence.
Course Prerequisites
Satisfactory completion of coursework and examinations in Mathematical Economics, Statistics, Economics, with Financial Mathematics is strongly recommended.
Teaching Methods
Lectures, Laboratory activities at the Decision LAB, Seminars and Workshops
Assessment Methods
Written and oral examination
Evaluation criteria:
30 cum laude: complete, in-depth and critical knowledge of the topics, excellent language skills, complete and original interpretative ability, full ability to independently apply knowledge to solve the proposed problems;
28 - 30: complete and in-depth knowledge of the topics, excellent language skills, complete and effective interpretative skills, able to independently apply the knowledge to solve the proposed problems;
24 - 27: knowledge of the topics with a good degree of mastery, good command of the language, correct and sure interpretative ability, good ability to correctly apply most of the knowledge to solve the proposed problems;
20 - 23: adequate knowledge of the topics but limited mastery of the same, satisfactory language skills, correct interpretative ability, more than sufficient ability to independently apply the knowledge to solve the proposed problems;
18 - 19: basic knowledge of the main topics, basic knowledge of the technical language, sufficient interpretative ability, sufficient ability to apply the acquired basic knowledge;
Texts
Course materials prepared by Professors Massimiliano Ferrara and Bruno Antonio Pansera, including slides and teaching materials in the form of scientific articles and written works by the instructor.
PS: Students not attending the course can obtain teaching materials by contacting Professor Pansera by email: bruno.pansera@unirc.it
Contents
MODULE I - FOUNDATIONS OF ADVANCED MATHEMATICS AND MULTIVARIATE AND INFERENTIAL STATISTICS
- Mathematical Analysis: Functions of two or more variables. Quadratic forms, unconstrained optimization problems. Constrained optimization problems, inequality constraints. Differential equations with closed-form solutions.
- Bivariate Analysis: Contingency tables, sample correlation coefficient.
- Multivariate Random Variables: Bivariate random variables, joint and marginal distribution functions, joint and marginal densities: discrete densities and two-way tables, continuous densities and volume formula. Independence of random variables. Expected value of the product of two random variables. Covariance and linear correlation coefficient and their properties. Introduction to the bivariate Gaussian model, 2-D uniform distribution, n-variate random variables, multinomial distribution.
- Inferential Statistics: Tests and confidence intervals for the proportion of a large Bernoulli population. Tests for comparing the means of two normal or large populations. Tests for comparing the variances of two normal populations. Tests for comparing the proportions of two large Bernoulli populations.
MODULE II - FINANCIAL MATHEMATICS FUNDAMENTALS
1. Basic Concepts
- Time value of money and opportunity cost of capital
- Compounding and discounting
- Simple vs compound interest regimes
2. Core Tools
- Annuities and perpetuities
- Interest rates (nominal, effective, APR)
- Fisher relation and real rates
MODULE III - INVESTMENT APPRAISAL
3. Investment Analysis Framework
- Incremental cash flows
- Economic life and terminal value
- Treatment of common costs and sunk costs
4. Valuation Criteria
- NPV, IRR, EVA, Payback
- IRR pitfalls and limitations
- Project selection and ranking
MODULE IV - PORTFOLIO THEORY
5. Risk and Return Measures
- Return calculations and volatility
- Empirical distribution of returns
6. Markowitz Model
- Mean-variance framework
- Correlation and diversification
- Efficient frontier
7. Portfolio Optimization
- Portfolios with risk-free assets
- Utility functions and optimal choice
- Asset allocation strategies
MODULE V - EQUILIBRIUM MODELS
8. CAPM and Single-Factor Models
- Capital Market Line and Security Market Line
- Sharpe's single-index model and beta
- Systematic vs idiosyncratic risk
9. Multi-Factor Models
- Arbitrage Pricing Theory
- Multiple risk factors
- Factor portfolios
MODULE VI - ADVANCED TECHNIQUES
10. Parameter Estimation
- Estimation error and resampling techniques
- EWMA models for volatility
- Practical implementation
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