Markets with transaction costs. Mathematical theory. (Q930275)

This book contains an introduction to the mathematical theory of financial markets with proportional transaction costs. The main subjects are: the Leland approach to the hedging of contingent claims based on approximate replication, arbitrage theory for markets with proportional transaction costs based on a geometric approach and the consumption-investment problem analysed using viscosity solutions of the Hamilton-Jacobi-Bellman equation. This is the first book that covers this subject and thus is very useful for scientists and researchers in 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.