Introduction to probability and mathematical statistics with a special focus on economic and financial applications.
Contenuto del corso
Time value of money, interests and financial schemes (simple interest, compounded interest, continuous interests etc.)
Amortization tables.
Internal rate of return and Present Value to judge investment convenience.
Bonds pricing, duration, convexity.
Excel programming and basics of computer coding.
D.Lovelock, M.Mendel, A.L. Wright – An Introduction to the Mathematics of Money, Springer Chapters: 1, 2, 3, 4, 5, 6, 8
Obiettivi Formativi
The students will be able to solve simple problems where the random model is required for economic and financial applications. They will be able to formalize the problem, solve it and present their results.
Obiettivi Formativi
Learn basic concepts like time value of money, discounting and compounding, basic financial modelling.
Learn how to choose between different financial investments using mathematical thinking.
Prerequisiti
Basic Calculus
Prerequisiti
Basic Mathematics (first and second order derivative, Taylor's expansion, limits, logarithms)
Metodi Didattici
Classroom lectures and homeworks
Metodi Didattici
On site or Online lessons (according to Covid-19 dispositions), and monthly assignments (not compulsory)
Altre Informazioni
Attendance (virtual or in presence) is stongly suggested
Altre Informazioni
First lesson of the week will usually be theory. Second lesson of the week will be exercises and coding.
Modalità di verifica apprendimento
Homeworks, projects and oral exam
Modalità di verifica apprendimento
Written final exam with exercises
Programma del corso
Random models. Combinatorics, probability and conditional probability, independency, Bayes formula will be introduced motivated by the applications in economics and financial markets. Lotteries and probabilistic paradoxes.
Discrete random variables, Bernoulli, Binomial, Geometric, Poisson distributions.
Applications to statistical inference, VaR, financial default.
Elementary stochastic processes: random walk and Markov chain. Applications: asset price models, option pricing, credit rating.
Continuous random variables. Basic elements of integration theory. Uniform, Exponential, Normal distributions.
Expectation, variance, skewness, curtosis.
Gaussian approximation. Application to finance and risk management.
Programma del corso
-time value of money
-interests
-financial schemes
-amortization tables
-IRR
-duration, convexity
-bonds pricing
-Excel coding
-recap of linear algebra