Enlargement of Filtration with Finance in View / by Anna Aksamit, Monique Jeanblanc.

Format:

Book

Author/Creator:

Aksamit, Anna., Author.

Jeanblanc, Monique., Author.

Series:

SpringerBriefs in Quantitative Finance, 2192-7006

Language:

English

Subjects (All):

Economics, Mathematical.

Probabilities.

Quantitative Finance.

Probability Theory and Stochastic Processes.

Local Subjects:

Quantitative Finance.

Probability Theory and Stochastic Processes.

Physical Description:

1 online resource (X, 150 p.)

Edition:

1st ed. 2017.

Place of Publication:

Cham : Springer International Publishing : Imprint: Springer, 2017.

Summary:

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.

Contents:

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

Solutions to some exercises

Indexes.

Notes:

Includes bibliographical references and index.

ISBN:

3-319-41255-8