Mathematical Finance: Theory Review and Exercises

The book collects over 120 exercises on different subjects of Mathematical Finance, including Option Pricing, Risk Theory, and Interest Rate Models. Many of the exercises are solved, while others are only proposed. Every chapter contains an introductory section illustrating the main theoretical results necessary to solve the exercises. The book is intended as an exercise textbook to accompany graduate courses in mathematical finance offered at many universities as part of degree programs in Applied and Industrial Mathematics, Mathematical Engineering, and Quantitative Finance.

Offers substantially more exercises on continuous time than do other textbooks Includes three completely new chapters (one on Arbitrage Theory and Incompleteness, one on Risk Measures, and one on Stochastic Volatility Models and Models with jumps) Presents a middle ground between the stochastic and the analytic approach to option pricing and hedging at a reasonable, but not trivial, mathematical level Includes supplementary material: sn.pub/extras

Autorentext

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.

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.