Enlargement of Filtration with Finance in View

ISBN-13: 9783319412542 / Angielski / Miękka / 2017 / 150 str.

Anna Aksamit; Monique Jeanblanc

Opis

In addition to presenting the basic theory of enlargement of filtrations, this book also includes new material and applications to finance. The main results are applied to give conditions which ensure that new information does not provide arbitrage opportunities, and in those cases where the arbitrages exist, they are explicitly constructed. Numerous examples are provided together with a list of recent papers on the subject. The presentation has been kept as simple as possible. In particular, sophisticated new results are given without proofs.Addressing the question of how to model and study new information flows, the theory of enlargement of filtrations is used in credit risk modeling, insider trading and in the study of asymmetric information.
This book fills a gap in the literature and will be useful to students and researchers interested in the role of information, both in financial mathematics and in econometric science.

Recenzje

"This book presents a succinct exposition on the theory of filtration enlargements. ... The book delivers a systematic and updated account of the subject. There is a long list of papers in the references, including the authors' own contributions, providing a broad perspective. ... it is an excellent guide from which the reader will gain a global view of the field." (Erick Treviño-Aguilar, Mathematical Reviews, August, 2018)
"The book is devoted to enlargement of filtration - an important tool and field of study in the theory of stochastic processes. ... The book is a useful reading for students and professionals in theory and practice of finance." (Pavel Stoynov, zbMATH 1397.91003, 2018)

Spis treści

Theory of Stochastic Processes.- Semimartingales.- Change of probability and Girsanov’s Theorem.- Projections and Dual Projections.- Exercises .-Bibliographic.- Compensators of Random .- Compensator of a Default Indicator in its own Filtration.- Compensator of the Default Process in a General Setting .- Cox Processes and Extensions.- Study of Azéma’s supermartingale in general setting.- Exercices .- Bibliographic Notes.-Immersion Property.- Immersion of Immersion in a Progressive Enlargement of Filtration.- Multidefaults Setting.-Exercices .- Bibliographic.- Initial Enlargement.- Brownian and Poisson Bridges.- Insider Trading.- Enlargement of Filtration setting.- Yor’s Method.-Jacod’s Absolute Continuity Condition.- Jacod’s Equivalence Condition.- List of examples in the Literature.- Bibliographic Notes.- Progressive Enlargement.- G-semimartingale decomposition of F-martingales before t.- Honest Times.- (E)-times.- 5.4 Pseudo-stopping Times.- Predictable Representation property.-Enlargement with the filtration generated by a continuous process .- Arbitrages in a progressive Enlargement.- Applications of (E)-times to Finance.- Exercises.- Bibliographic Notes.- Solutions to some exercises.- Indexes.

Blurb

This volume presents classical results of the theory of enlargement of filtration. The focus is on the behavior of martingales with respect to the enlarged filtration and related objects. The study is conducted in various contexts including immersion, progressive enlargement with a random time and initial enlargement with a random variable. 

The aim of this book is to collect the main mathematical results (with proofs) previously spread among numerous papers, great part of which is only available in French. Many examples and applications to finance, in particular to credit risk modelling and the study of asymmetric information, are provided to illustrate the theory. A detailed summary of further connections and applications is given in bibliographic notes which enables to deepen study of the topic. 

This book fills a gap in the literature and serves as a guide for graduate students and researchers interested in the role of information in financial mathematics and in econometric science. A basic knowledge of the general theory of stochastic processes is assumed as a prerequisite.