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Finanziaria e Attuariale, Inferenza Statistica, Statistica per il Risk Management are recommended.
The course will present the main aspects of the quantitative theory of modern finance. The students will gain a knowledge sufficient to understand and (up to some point) manage the main financial models currently used at academic and professional levels to price derivative instruments, to define hedging strategies, to measure and control risks.
- Stochastic processes - Martingales - Brownian motion and related processes (Brownian motion with drift, geometric Brownian motion, Brownian bridge) - Riemann and Stieltjes (deterministic) integrals: definition and properties - Overview of ordinary differential equations - Ito (stochastic) integrals: definition and properties - Ito's lemma: "stochastic differential" and (deterministic) differential of a function - Stochastic differential equations: introduction, analitic and numerical solution methods of simple cases - Changes of probabilities: from random variables (change of the mean) to stochastic processes (change of the drift through the Girsanov theorem and the Radon-Nikodym derivative)
Elementary Stochastic Calculus With Finance in View, Thomas Mikosch, World Scientific, 1998, ISBN: 9789810235437. Teaching resources available on the university web site (comunità didattica) of the course.
The course will be taught through traditional lectures and tutorials.
The exam consists of a written and an oral part. Homeworks will contribute to the final valuation.