Stochastic models of financial mathematics (Q2825532)

These lecture notes are based on a graduate course given for several years at Vilnius University as part of the Master's program ``Financial and Actuarial Mathematics''.NEWLINENEWLINEThe book consists of three chapters. Chapter 1 gives an overview of the basics of stochastic analysis, including Brownian motion, stochastic integration, martingales, Itô processes and general Itô's formula, stochastic differential equations and the Girsanov theorem. Chapter 2 is devoted to the Black-Scholes model. It starts with the description of the portfolio and self-financing trading strategies, and continues with the option pricing problem, the Black-Scholes formula, option Greeks, risk-neutral probabilities, American and exotic options. Chapter 3 contains the description of the models of interest rate: the Vašiček model, the Cox-Ingersoll-Ross model and the Heath-Jarrow-Morton model.NEWLINENEWLINEThe book is written at a high mathematical level, however very clearly for the reader, and will be useful both for undergraduate and post graduate students, practitioners and everybody who wants to study the basic properties of financial markets with continuous time.