The first part of the course provides the fundamentals of financial mathematics under certainty conditions. The second part is devoted to elements of probability theory, revisited from a financial point of view. This will allow students to consider financial mathematics applications in stochastic frameworks (i.e. applications in portfolio theory and in actuarial fields). At the end of the course students will be able to:

• knowing and managing interest, discount, final value, present value, rates, capitalization and discount factors;

• using different accumulation and discount functions;

• linking the properties of financial functions with arbitrage free assumptions under certainty conditions;

• making financial evalutations under no flat yield curves;

• evaluating annuities;

• writing amortization schedules;

• evaluating enterpreneurial projects;

• giving a financial meaning to probabilities and proving the fundamental probability theorems with the no arbitrage assumption;

• knowing the ways to characterize (discrete and continuous) random variables probability distributions;

• knowing the most important synthetic distribution indices and giving them a financial meaning when the random variables are stochastic assets returns;

• applying the financial and probabilistic tools to decisions under uncertainty (in particular to portfolio choices and to evaluation of life insurance premiums).

Soft skills:

• the student should reach a financial literacy level so that he will be able to identifying and analyzing financial information, solving financial problems;

• students should become aware of the importance of risk in financial investing, in financial planning and in stochastic asset pricing;

• topics handled during the course are fundamental for advanced course in quantitative finance;

• both under certainty and uncertainty we give relevance to the no arbitrage condition that is fundamental in stochastic asset pricing in finance.