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.

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.