Mathematical Finance

Emanuela Rosazza Gianin is Professor of Mathematical Finance at Department of Statistics and Quantitative Methods at the University of Milano Bicocca in Italy. Before working there with different positions, she worked at University of Naples Federico II, still in Italy, as Assistant Professor. Her research interests focus on different aspects of risk measures, insurance premia and pricing, as well as on Backward Stochastic Differential Equations and their applications to Mathematical Finance. She has published about 30 papers in international scientific journals and two textbooks for Springer.Carlo Sgarra is Associate Professor of Mathematical Finance at Politecnico di Milano. The main subjects of his research are exotic option pricing, valuation problems in incomplete market models, in particular stochastic volatility models, models with jumps and models with transaction cost. His most recent projects are focused on energy market models and pricing and hedging of energy commodity derivatives: parameter estimation methods and risk premium valuation for different model classes. He published about 30 papers on international journals and three textbooks on Mathematical Finance.

“This is the second edition of a textbook originally written in 2013. Similarly to the first edition, the volume draws on the extensive teaching experience of the two authors by presenting a wide range of (solved and unsolved) exercises. ... This book can therefore represent a useful source of inspiration for anyone lecturing on mathematical finance.” (Claudio Fontana, zbMATH 1529.91003, 2024)

• - 1. Short Review of Probability and of Stochastic Processes. - 2. Portfolio Optimization in Discrete-Time Models. - 3. Binomial Model for Option Pricing. - 4. Absence of Arbitrage and Completeness of Market Models. - 5. Itô’s Formula and Stochastic Differential Equations. - 6. Partial Differential Equations in Finance. - 7. Black-Scholes Model for Option Pricing and Hedging Strategies. - 8. American Options. - 9. Exotic Options. - 10. Interest Rate Models. - 11. Pricing Models Beyond Black-Scholes. - 12. Risk Measures: Value at Risk and Beyond.