Synopses & Reviews
The book is the first monograph on this highly important subject.
Review
From the reviews: "This book contains an introduction to the mathematical theory of financial markets with proportional transaction costs. ... This is the first book that covers this subject and thus is very useful for scientists and researchers on this field. One can find useful information in the bibliographical comments at the end of the book, and in the appendix there are results from convex analysis that are used for some of the proofs, an introduction to the Skorokhod problem and stochastic differential equations with reflections." (Nikolaos Halidias, Zentralblatt MATH, Vol. 1186, 2010) "It is the first book to compile the results from a substantial body of literature coherently in a single volume, and thus may be valuable to researchers looking for a theoretical foundation for their models. ... the authors have incorporated up-to-date results. ... Kabanov and Safarin have succeeded in creating the first book to summarize some of the major contributions in the mathematical finance literature on proportional transaction costs. ... I recommend it as a stepping stone to the research field of transaction costs." (Evert Wipplinger, Financial Markets and Portfolio Management, Vol. 25, 2011)
Review
From the reviews:
"This book contains an introduction to the mathematical theory of financial markets with proportional transaction costs. ... This is the first book that covers this subject and thus is very useful for scientists and researchers on this field. One can find useful information in the bibliographical comments at the end of the book, and in the appendix there are results from convex analysis that are used for some of the proofs, an introduction to the Skorokhod problem and stochastic differential equations with reflections." (Nikolaos Halidias, Zentralblatt MATH, Vol. 1186, 2010)
"It is the first book to compile the results from a substantial body of literature coherently in a single volume, and thus may be valuable to researchers looking for a theoretical foundation for their models. ... the authors have incorporated up-to-date results. ... Kabanov and Safarin have succeeded in creating the first book to summarize some of the major contributions in the mathematical finance literature on proportional transaction costs. ... I recommend it as a stepping stone to the research field of transaction costs." (Evert Wipplinger, Financial Markets and Portfolio Management, Vol. 25, 2011)
Synopsis
The central mathematical concept in the theory of frictionless market is a martingale measure.
The authors argue that for financial markets with proportional transaction costs this concept should be replaced by the concept of consistent price system which is a martingale evolving in the duals to the solvency cones. The book presents a unified treatment of various problems arising in the theory of financial markets with friction. It gives a succinct account of arbitrage theory for financial markets with and without transaction costs based on a synthesis of ideas from the finite-dimensional geometry, functional analysis, and stochastic processes. For practitioners working with low-liquid markets the chapter on Leland's approximate hedging strategies will be of especial interest.
The book is supplemented by an appendix that provides a toolbox containing auxiliary results from various branches of mathematics used in the proofs.
Synopsis
This book presents a unified treatment of various problems arising in the theory of financial markets with friction. It gives a succinct account of arbitrage theory for financial markets with and without transaction costs based on a synthesis of ideas.
Table of Contents
1.Approximative Hedging.- 2.Arbitrage Theory for Frictionless Markets.- 3.Arbitrage Theory under Transaction Costs.- 4.Consumption--Investment Problems.- A.Appendices: A.1.Facts from Convex Analysis.- A.2.Césaro Convergence.- A.3.Facts from Probability.- A.4.Measurable Selection.- A.5.Fatou-Convergence and Bipolar Theorem in L0.- A.6.Skorohod Problem and SDE with Reflections.- B.Bibliographical comments.- References.