LEADER 04553nam 22005055 450 001 996418256803316 005 20200716234053.0 010 $a3-030-39724-6 024 7 $a10.1007/978-3-030-39724-1 035 $a(CKB)4100000011343475 035 $a(DE-He213)978-3-030-39724-1 035 $a(MiAaPQ)EBC6310591 035 $a(PPN)269147470 035 $a(EXLCZ)994100000011343475 100 $a20200716d2020 u| 0 101 0 $aeng 135 $aurnn|008mamaa 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aMarket-Consistent Prices$b[electronic resource] $eAn Introduction to Arbitrage Theory /$fby Pablo Koch-Medina, Cosimo Munari 205 $a1st ed. 2020. 210 1$aCham :$cSpringer International Publishing :$cImprint: Birkhäuser,$d2020. 215 $a1 online resource (XIX, 446 p. 44 illus., 1 illus. in color.) 311 $a3-030-39722-X 327 $aIntroduction -- A full picture in the simplest case -- Part I: One-period models -- Finite probability spaces.-Random variables -- The space of random variables -- Separation theorems -- Positive linear functionals -- One-period models: The Law of One Price -- One-period models: The Fundamental Theorem of Asset Pricing -- One-period models: Incomplete markets -- Part II: Multi-period models -- Information and measurability.-Conditional probabilities and conditional expectation -- Stochastic processes and martingales -- Multi-period models: The Law of One Price -- Multi-period models: The Fundamental Theorem of Asset Pricing -- Multi-period models: Incomplete markets -- The Cox-Ross-Rubinstein model -- Optimal stopping -- Multi-period models: American claims -- Part III: The Black-Scholes formula -- The central limit theorem -- The Black-Scholes formula -- Appendices -- A Linear algebra -- B Normed spaces -- C. Combinatorics. 330 $aArbitrage Theory provides the foundation for the pricing of financial derivatives and has become indispensable in both financial theory and financial practice. This textbook offers a rigorous and comprehensive introduction to the mathematics of arbitrage pricing in a discrete-time, finite-state economy in which a finite number of securities are traded. In a first step, various versions of the Fundamental Theorem of Asset Pricing, i.e., characterizations of when a market does not admit arbitrage opportunities, are proved. The book then focuses on incomplete markets where the main concern is to obtain a precise description of the set of ?market-consistent? prices for nontraded financial contracts, i.e. the set of prices at which such contracts could be transacted between rational agents. Both European-type and American-type contracts are considered. A distinguishing feature of this book is its emphasis on market-consistent prices and a systematic description of pricing rules, also at intermediate dates. The benefits of this approach are most evident in the treatment of American options, which is novel in terms of both the presentation and the scope, while also presenting new results. The focus on discrete-time, finite-state models makes it possible to cover all relevant topics while requiring only a moderate mathematical background on the part of the reader. The book will appeal to mathematical finance and financial economics students seeking an elementary but rigorous introduction to the subject; mathematics and physics students looking for an opportunity to get acquainted with a modern applied topic; and mathematicians, physicists and quantitatively inclined economists working or planning to work in the financial industry. 606 $aProbabilities 606 $aGame theory 606 $aProbability Theory and Stochastic Processes$3https://scigraph.springernature.com/ontologies/product-market-codes/M27004 606 $aGame Theory, Economics, Social and Behav. Sciences$3https://scigraph.springernature.com/ontologies/product-market-codes/M13011 615 0$aProbabilities. 615 0$aGame theory. 615 14$aProbability Theory and Stochastic Processes. 615 24$aGame Theory, Economics, Social and Behav. Sciences. 676 $a332.645 700 $aKoch-Medina$b Pablo$4aut$4http://id.loc.gov/vocabulary/relators/aut$0148629 702 $aMunari$b Cosimo$4aut$4http://id.loc.gov/vocabulary/relators/aut 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a996418256803316 996 $aMarket-Consistent Prices$92135492 997 $aUNISA