Business sciences

Definition and classification of financial operations. Basic financial operations. Principle of financial equivalence. Assumptions of the ideal market. Characteristics of real financial markets. Schemes of investment and anticipation financial operations. Assumptions regarding price functions. Capitalization factor. Discounting factor. Interest. Effective interest rate. Discount. Effective discount rate. Spot and forward financial operations. Properties of value functions in the context of forward schemes. Relationship between spot and forward operations (in the case of two periods). No-arbitrage condition. Market structure based on interest rates. Financial regimes. Financial regime of compound capitalization (periodic rate, variable rates, average rate). Equivalent rates. Nominal interest rate convertible. Instantaneous interest intensity. Nominal discount rate convertible. Instantaneous discount intensity. Interest force for financial laws of one variable. Interest force for financial laws of two variables. Divisibility. Uniformity. Financial regime of simple capitalization. Financial regime of commercial discounting. Complex financial operations. Annuities. Valuation of an annuity. Internal rate of return. Classification of annuities. Present values and amounts for immediate, deferred, advanced, postponed, whole, and fractional annuities. Present values for perpetuities. Present values and amounts for continuous annuities. Mixed capitalization (overview). Determining the number of installments, the installment amount, and the interest rate. Rate search problem: iterative method, interpolation method, and successive approximation method. Temporal and variability indices. Maturity. Financial average maturity. Arithmetic average maturity. Duration: definition, properties, and financial interpretation. Duration of fixed-coupon securities. Convexity: definition and classification. Bond loans. Duration of: bonds (TCN, TCF), bond portfolios (with examples), immediate deferred annuity with constant installments and properties. Convexity. Capital formation and amortizations. Issues related to capital formation. Loan contract (generalities). Residual debt. Settled debt. Capital portion. Interest portion. Installment. Amortization: classification. Amortization with periodic interest payments and final capital repayment. Progressive amortization. Uniform amortization. Amortization with two rates. Amortization with prepaid interest.

In order to successfully engage with the Financial Mathematics course, students should have a fundamental understanding of calculus, particularly in areas such as algebra, limits, derivatives, integrals, and basic concepts of statistics and probability. Familiarity with the principles of economics, as well as the fundamental concepts of banking and financial operations, is also recommended. Knowledge of key calculation tools, such as scientific calculators or spreadsheet software, is advisable to facilitate the practical application of the methodologies covered throughout the course

• Teaching material developed for the course (by Prof. Sergio Bianchi) • M. Frezza, Esercizi di Matematica Finanziaria svolti e commentati, McGraw Hill, 2019 • Past exams

Attendance to the course is strongly recommended

A comprehensive written exam aimed at assessing students' understanding of fundamental mathematical concepts and their application to economic and financial problems. The exam may include both theoretical questions and practical problem-solving exercises.

The course will be delivered through a combination of the following teaching methods: - Lectures Formal classes where the instructor presents key mathematical concepts, theories, and techniques relevant to economics and finance. Lectures are designed to build foundational understanding and provide structured explanations of the course material. - Interactive Exercises and In-Class Activities During selected lectures or tutorials, students may engage in guided exercises or collaborative problem-solving tasks to reinforce comprehension and encourage active participation. - Assignments and Homework Regular problem sets will be assigned to help students consolidate their understanding and apply the techniques learned in class to practical problems.

Definition and classification of financial operations. Basic financial operations. Principle of financial equivalence. Assumptions of the ideal market. Characteristics of real financial markets. Schemes of investment and anticipation financial operations. Assumptions regarding price functions. Capitalization factor. Discounting factor. Interest. Effective interest rate. Discount. Effective discount rate. Spot and forward financial operations. Properties of value functions in the context of forward schemes. Relationship between spot and forward operations (in the case of two periods). No-arbitrage condition. Market structure based on interest rates. Financial regimes. Financial regime of compound capitalization (periodic rate, variable rates, average rate). Equivalent rates. Nominal interest rate convertible. Instantaneous interest intensity. Nominal discount rate convertible. Instantaneous discount intensity. Interest force for financial laws of one variable. Interest force for financial laws of two variables. Divisibility. Uniformity. Financial regime of simple capitalization. Financial regime of commercial discounting. Complex financial operations. Annuities. Valuation of an annuity. Internal rate of return. Classification of annuities. Present values and amounts for immediate, deferred, advanced, postponed, whole, and fractional annuities. Present values for perpetuities. Present values and amounts for continuous annuities. Mixed capitalization (overview). Determining the number of installments, the installment amount, and the interest rate. Rate search problem: iterative method, interpolation method, and successive approximation method. Temporal and variability indices. Maturity. Financial average maturity. Arithmetic average maturity. Duration: definition, properties, and financial interpretation. Duration of fixed-coupon securities. Convexity: definition and classification. Bond loans. Duration of: bonds (TCN, TCF), bond portfolios (with examples), immediate deferred annuity with constant installments and properties. Convexity. Capital formation and amortizations. Issues related to capital formation. Loan contract (generalities). Residual debt. Settled debt. Capital portion. Interest portion. Installment. Amortization: classification. Amortization with periodic interest payments and final capital repayment. Progressive amortization. Uniform amortization. Amortization with two rates. Amortization with prepaid interest.

In order to successfully engage with the Financial Mathematics course, students should have a fundamental understanding of calculus, particularly in areas such as algebra, limits, derivatives, integrals, and basic concepts of statistics and probability. Familiarity with the principles of economics, as well as the fundamental concepts of banking and financial operations, is also recommended. Knowledge of key calculation tools, such as scientific calculators or spreadsheet software, is advisable to facilitate the practical application of the methodologies covered throughout the course

• Teaching material developed for the course (by Prof. Sergio Bianchi) • M. Frezza, Esercizi di Matematica Finanziaria svolti e commentati, McGraw Hill, 2019 • Past exams

Attendance to the course is strongly recommended

A comprehensive written exam aimed at assessing students' understanding of fundamental mathematical concepts and their application to economic and financial problems. The exam may include both theoretical questions and practical problem-solving exercises.

The course will be delivered through a combination of the following teaching methods: - Lectures Formal classes where the instructor presents key mathematical concepts, theories, and techniques relevant to economics and finance. Lectures are designed to build foundational understanding and provide structured explanations of the course material. - Interactive Exercises and In-Class Activities During selected lectures or tutorials, students may engage in guided exercises or collaborative problem-solving tasks to reinforce comprehension and encourage active participation. - Assignments and Homework Regular problem sets will be assigned to help students consolidate their understanding and apply the techniques learned in class to practical problems.