The mathematics of arbitrage (Q2493436)

The book consists of two parts. Part I contains the ``guided tour'' through the mathematical theory of finances which is divided into eight chapters. Chapters 1--4 give expositions of basic topics of mathematical finance and are kept at an elementary technical level. From Chapter 5 on, the level of technical sophistication increases rather steeply. Chapter 5 starts with D. Krep's version of the Fundamental Theorem of Asset Pricing involving the notion of ``No Free Lunch''. In the next chapters several different proofs of the Dalang-Morton-Willinger theorem are included, in particular, the proof based on the notion of ``measurably parameterised subsequences''. Also, a quick overview of stochastic integration is presented. Part II consists of updated versions of seven papers of the authors devoted to financial mathematics with a number of corrections. Among them ``A general version of the Fundamental Theorem of Asset Pricing', ``The existence of absolutely continuous local martingale measures'' and some others that became classics in mathematical finance.