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Markets with Transaction Costs: Mathematical Theory (Springer Finance)by Yuri Kabanov
Synopses & Reviews
The book is the first monograph on this highly important subject.
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.
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.
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