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Author: Anna Aksamit Publisher: Springer ISBN: 3319412558 Category : Mathematics Languages : en Pages : 155
Book Description
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.
Author: Anna Aksamit Publisher: Springer ISBN: 3319412558 Category : Mathematics Languages : en Pages : 155
Book Description
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.
Author: Jean-Michel Morel Publisher: Springer Nature ISBN: 3031122445 Category : Mathematics Languages : en Pages : 629
Book Description
This volume is an original collection of articles by 44 leading mathematicians on the theme of the future of the discipline. The contributions range from musings on the future of specific fields, to analyses of the history of the discipline, to discussions of open problems and conjectures, including first solutions of unresolved problems. Interestingly, the topics do not cover all of mathematics, but only those deemed most worthy to reflect on for future generations. These topics encompass the most active parts of pure and applied mathematics, including algebraic geometry, probability, logic, optimization, finance, topology, partial differential equations, category theory, number theory, differential geometry, dynamical systems, artificial intelligence, theory of groups, mathematical physics and statistics.
Author: Thomas Mikosch Publisher: World Scientific ISBN: 9789810235437 Category : Mathematics Languages : en Pages : 230
Book Description
Modelling with the Ito integral or stochastic differential equations has become increasingly important in various applied fields, including physics, biology, chemistry and finance. However, stochastic calculus is based on a deep mathematical theory. This book is suitable for the reader without a deep mathematical background. It gives an elementary introduction to that area of probability theory, without burdening the reader with a great deal of measure theory. Applications are taken from stochastic finance. In particular, the Black -- Scholes option pricing formula is derived. The book can serve as a text for a course on stochastic calculus for non-mathematicians or as elementary reading material for anyone who wants to learn about Ito calculus and/or stochastic finance.
Author: Samuel N. Cohen Publisher: Springer Nature ISBN: 3030222853 Category : Mathematics Languages : en Pages : 303
Book Description
This collection of selected, revised and extended contributions resulted from a Workshop on BSDEs, SPDEs and their Applications that took place in Edinburgh, Scotland, July 2017 and included the 8th World Symposium on BSDEs. The volume addresses recent advances involving backward stochastic differential equations (BSDEs) and stochastic partial differential equations (SPDEs). These equations are of fundamental importance in modelling of biological, physical and economic systems, and underpin many problems in control of random systems, mathematical finance, stochastic filtering and data assimilation. The papers in this volume seek to understand these equations, and to use them to build our understanding in other areas of mathematics. This volume will be of interest to those working at the forefront of modern probability theory, both established researchers and graduate students.
Author: Jin Cheng Publisher: Springer Nature ISBN: 9811655766 Category : Technology & Engineering Languages : en Pages : 191
Book Description
This volume includes selected technical papers presented at the Forum “Math-for-Industry” 2018. The papers written by eminent researchers and academics working in the area of industrial mathematics from the viewpoint of financial mathematics, machine learning, neural networks, inverse problems, stochastic modelling, etc., discuss how the ingenuity of science, technology, engineering and mathematics are and will be expected to be utilized. This volume focuses on the role that mathematics-for-industry can play in interdisciplinary research to develop new methods. The contents are useful for researchers both in academia and industry working in interdisciplinary sectors.
Author: Charles-albert Lehalle Publisher: World Scientific ISBN: 9811252599 Category : Business & Economics Languages : en Pages : 365
Book Description
Financial Markets in Practice: From Post-Crisis Intermediation to FinTechs delivers an overview of the development of risk-transformation undertaken by the financial services industry from the perspective of quantitative finance. It provides an instructional and comprehensive explanation of the structure of the financial system as a network of risk suppliers and risk consumers, where different categories of market participants buy, transform, net, and re-sell different kinds of risks. This risk-transformation oriented view is supported by the changes that followed the last global financial crisis: consumers of financial products asked for less complex risk transformations, regulators demanded limiting risks inside financial institutions to the maximum extent possible, and market participants turned to run mass market-like businesses and away from bespoke 'haute couture'-like businesses.This book portrays the network of intermediaries that compose the financial system, describes their most common business models, explains the exact role of each kind of market participant, and underlines the interaction between them. It seeks to reveal the potential disintermediation that could occur inside the financial sector, led by FinTechs and Artificial Intelligence-based innovations.Readers are invited to reconsider the role of market participants in the post-crisis world and are prepared for the next wave of changes driven by data science, AI, and blockchain. Amid these innovations, quantitative finance will be increasingly involved in all aspects of the financial system. This handy resource helps practitioners from both the buy-side and sell-side gain insights to, and provides an overview of, business models in the financial system from an intermediation perspective, and guides students to comprehensively understand the complex ecosystem in which they will evolve.
Author: Catherine Donati-Martin Publisher: Springer Nature ISBN: 3030285359 Category : Mathematics Languages : en Pages : 562
Book Description
This milestone 50th volume of the "Séminaire de Probabilités" pays tribute with a series of memorial texts to one of its former editors, Jacques Azéma, who passed away in January. The founders of the "Séminaire de Strasbourg", which included Jacques Azéma, probably had no idea of the possible longevity and success of the process they initiated in 1967. Continuing in this long tradition, this volume contains contributions on state-of-art research on Brownian filtrations, stochastic differential equations and their applications, regularity structures, quantum diffusion, interlacing diffusions, mod-Ø convergence, Markov soup, stochastic billiards and other current streams of research.
Author: Ying Jiao Publisher: Springer Nature ISBN: 981151576X Category : Mathematics Languages : en Pages : 253
Book Description
This volume presents a collection of lecture notes of mini-courses taught at BICMR Summer School of Financial Mathematics, from May 29 to June 9, 2017. Each chapter is self-contained and corresponds to one mini-course which deals with a distinguished topic, such as branching processes, enlargement of filtrations, Hawkes processes, copula models and valuation adjustment analysis, whereas the global topics cover a wide range of advanced subjects in financial mathematics, from both theoretical and practical points of view. The authors include world-leading specialists in the domain and also young active researchers. This book will be helpful for students and those who work on probability and financial mathematics.
Author: Caroline Hillairet Publisher: Elsevier ISBN: 0081011776 Category : Business & Economics Languages : en Pages : 192
Book Description
Portfolio Optimization with Different Information Flow recalls the stochastic tools and results concerning the stochastic optimization theory and the enlargement filtration theory.The authors apply the theory of the enlargement of filtrations and solve the optimization problem. Two main types of enlargement of filtration are discussed: initial and progressive, using tools from various fields, such as from stochastic calculus and convex analysis, optimal stochastic control and backward stochastic differential equations. This theoretical and numerical analysis is applied in different market settings to provide a good basis for the understanding of portfolio optimization with different information flow. - Presents recent progress of stochastic portfolio optimization with exotic filtrations - Shows you how to apply the tools of the enlargement of filtrations to resolve the optimization problem - Uses tools from various fields from enlargement of filtration theory, stochastic calculus, convex analysis, optimal stochastic control, and backward stochastic differential equations
Author: Anna Aksamit
Author: Anna Aksamit
Author: Jean-Michel Morel
Author: Thomas Mikosch
Author: Samuel N. Cohen
Author: Jin Cheng
Author: Charles-albert Lehalle
Author: Catherine Donati-Martin
Author: Ying Jiao
Author: René Carmona
Author: Caroline Hillairet