Mathematical Finance

The book is conceived as a guide to solve exercises in Mathematical Finance and a complement to theoretical lectures. The potential audience consists of students in Applied Mathematics, Engineering and Economics, attending courses in Mathematical Finance. The most important subjects covered by this textbook are Pricing and Hedging of different classes of financial derivatives (European, American Exotic options, Fixed Income derivatives) in the most popular modeling frameworks, both in discrete and continuous time setting, like the Binomial and the Black-Scholes models. A Chapter on static portfolio optimization, one on pricing for more advanced models and one on Risk Measures complete the overview on the main issues presented in classical courses on Mathematical Finance. About one hundred exercises are proposed, and a large amount of them provides a detailed solution, while a few are left as an exercise to the reader. Every chapter includes a brief resume of the main theoretical results to apply. This textbook is the result of several years of teaching experience of both the authors.

Comprehensive guide to a deep understanding of the main subjects of graduate courses in Mathematical Finance A rich collection of exercises in Mathematical Finance with almost no competitors on the market Presents detailed solutions of exercises and a rigorous methodology

Autorentext

E manuela 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.

Inhalt

• 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.