03580nam a22004695i 4500001001800000003000900018005001700027007001500044008004100059020001800100024003500118050001400153072001500167072002300182072002300205082001200228100002800240245012200268250001800390264004600408300003400454336002600488337002600514338003600540347002400576490005100600505069900651520137901350650001702729650001302746650002902759650001902788650001702807650002602824650004902850650002202899710003402921773002002955776003602975830005103011856004803062978-1-4614-3582-2DE-He21320180115171518.0cr nn 008mamaa120423s2012 xxu| s |||| 0|eng d a97814614358227 a10.1007/978-1-4614-3582-22doi 4aHB135-147 7aKF2bicssc 7aMAT0030002bisacsh 7aBUS0270002bisacsh04a5192231 aRoman, Steven.eauthor.10aIntroduction to the Mathematics of Financeh[electronic resource] :bArbitrage and Option Pricing /cby Steven Roman. a2nd ed. 2012. 1aNew York, NY :bSpringer New York,c2012. aXVI, 288 p.bonline resource. atextbtxt2rdacontent acomputerbc2rdamedia aonline resourcebcr2rdacarrier atext filebPDF2rda1 aUndergraduate Texts in Mathematics,x0172-60560 aPreface -- Notation Key and Greek Alphabet -- 0 Introduction -- Part 1 Options and Arbitrage -- 1 Background on Options -- 2 An Aperitif on Arbitrage -- Part 2 Discrete-Time Pricing Models -- 3 Discrete Probability -- 4 Stochastic Processes, Filtrations and Martingales -- 5 Discrete-Time Pricing Models -- 6 The Binomial Model -- 7 Pricing Nonattainable Alternatives in an Incomplete Market -- 8 Optimal Stopping and American Options -- Part 3 the Black-Scholes Option Pricing Formula -- 9 Continuous Probability -- 10 The Black-Scholes Option Pricing Formula -- Appendix A: Convexity and the Separation Theorem -- Appendix B: Closed, Convex Cones -- Selected Solutions -- References -- Index. aThe Mathematics of Finance has been a hot topic ever since the discovery of the Black-Scholes option pricing formulas in 1973. Unfortunately, there are very few undergraduate textbooks in this area. This book is specifically written for advanced undergraduate or beginning graduate students in mathematics, finance or economics. This book concentrates on discrete derivative pricing models, culminating in a careful and complete derivation of the Black-Scholes option pricing formulas as a limiting case of the Cox-Ross-Rubinstein discrete model. This second edition is a complete rewrite of the first edition with significant changes to the topic organization, thus making the book flow much more smoothly. Several topics have been expanded such as the discussions of options, including the history of options, and pricing nonattainable alternatives. In this edition the material on probability has been condensed into fewer chapters, and the material on the capital asset pricing model has been removed. The mathematics is not watered down, but it is appropriate for the intended audience. Previous knowledge of measure theory is not needed and only a small amount of linear algebra is required. All necessary probability theory is developed throughout the book on a "need-to-know" basis. No background in finance is required, since the book contains a chapter on options. 0aMathematics. 0aFinance. 0aEconomics, Mathematical. 0aProbabilities.14aMathematics.24aQuantitative Finance.24aProbability Theory and Stochastic Processes.24aFinance, general.2 aSpringerLink (Online service)0 tSpringer eBooks08iPrinted edition:z9781461435815 0aUndergraduate Texts in Mathematics,x0172-605640uhttp://dx.doi.org/10.1007/978-1-4614-3582-2