الصفحة 1
الصفحة 1
Mathematics of Financial Markets
This book presents the mathematics that underpins pricing models for derivative securities, such as options, futures and swaps, in modern financial markets. The idealized continuous-time models built upon the famous Black-Scholes theory require sophisticated mathematical tools drawn from modern stochastic calculus. However, many of the underlying ideas can be explained more simply within a discrete-time framework. This is developed extensively in this substantially revised second edition to motivate the technically more demanding continuous-time theory, which includes a detailed analysis of the Black-Scholes model and its generalizations, American put options, term structure models and consumption-investment problems. The mathematics of martingales and stochastic calculus is developed where it is needed.
In Memoriam Paul-André Meyer - Séminaire de Probabilités XXXIX
The 39th volume of Séminaire de Probabilités is a tribute to the memory of Paul André Meyer. His life and achievements are recalled in this book, and tributes are paid by his friends and colleagues. This volume also contains mathematical contributions to classical and quantum stochastic calculus, the theory of processes, martingales and their applications to mathematical finance and Brownian motion. These contributions provide an overview on the current trends of stochastic calculus.
From Stochastic Calculus to Mathematical Finance : The Shiryaev Festschrift
The Festschrift is a collection of papers, including several surveys, written by his former students, co-authors and colleagues. These reflect the wide range of scientific interests of the teacher and his Moscow school. The topics range from the disorder problems to stochastic calculus and their applications to mathematical economics and finance. A full biobibliography of Shiryaev's works is included. The book represents the modern state of art of many aspects of a quickly maturing theory and will be an essential source and reading for researchers in this area.
Martingales and financial mathematics in discrete time
This book is entirely devoted to discrete time and provides a detailed introduction to the construction of the rigorous mathematical tools required for the evaluation of options in financial markets. Both theoretical and practical aspects are explored through multiple examples and exercises, for which complete solutions are provided. Particular attention is paid to the Cox, Ross and Rubinstein model in discrete time.
Martingale Methods in Financial Modelling
This book provides a comprehensive, self-contained and up-to-date treatment of the main topics in the theory of option pricing. The first part of the text starts with discrete-time models of financial markets, including the Cox-Ross-Rubinstein binomial model. The passage from discrete- to continuous-time models, done in the Black-Scholes model setting, assumes familiarity with basic ideas and results from stochastic calculus. However, an Appendix containing all the necessary results is included. This model setting is later generalized to cover standard and exotic options involving several assets and/or currencies. An outline of the general theory of arbitrage pricing is presented. The second part of the text is devoted to the term structure modelling and the pricing of interest-rate derivatives. The main emphasis is on models that can be made consistent with market pricing practice.
