LEADER 04389nam 22005655 450 001 9910254063503321 005 20200705163422.0 010 $a3-319-25589-4 024 7 $a10.1007/978-3-319-25589-7 035 $a(CKB)3710000000765119 035 $a(DE-He213)978-3-319-25589-7 035 $a(MiAaPQ)EBC6315808 035 $a(MiAaPQ)EBC5595405 035 $a(Au-PeEL)EBL5595405 035 $a(OCoLC)953818907 035 $a(PPN)194515443 035 $a(EXLCZ)993710000000765119 100 $a20160714d2016 u| 0 101 0 $aeng 135 $aurnn|008mamaa 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aStochastic Analysis for Finance with Simulations /$fby Geon Ho Choe 205 $a1st ed. 2016. 210 1$aCham :$cSpringer International Publishing :$cImprint: Springer,$d2016. 215 $a1 online resource (XXXII, 657 p. 189 illus., 107 illus. in color.) 225 1 $aUniversitext,$x0172-5939 311 $a3-319-25587-8 320 $aIncludes bibliographical references and index. 327 $aPreface -- Acknowledgements -- List of Figures -- List of Tables -- List of Simulations -- Fundamental Concepts -- Financial Derivatives -- The Lebesgue Integral -- Basic Probability Theory -- Conditional Expectation -- Stochastic Processes -- Brownian Motion -- Girsanov's Theorem -- The Reflection Principle of Brownian Motion -- The Ito Integral -- The Ito Formula -- Stochastic Differential Equations -- The Feynmann-Kac Theorem -- The Binomial Tree Method for Option Pricing -- The Black-Scholes-Merton Differential Equation -- The Martingale Method -- Pricing of Vanilla Options -- Pricing of Exotic Options -- American Options -- The Capital Asset Pricing Model -- Dynamic Programming -- Bond Pricing -- Interest Rate Models -- Numeraires -- Numerical Estimation of Volatility -- Time Series -- Random Numbers -- The Monte Carlo Method for Option Pricing -- Numerical Solution of the Black-Scholes-Merton Equation -- Numerical Solution of Stochastic Differential Equations. Appendices -- Solutions for Selected Problems -- Glossary -- References -- Index. . 330 $aThis book is an introduction to stochastic analysis and quantitative finance; it includes both theoretical and computational methods. Topics covered are stochastic calculus, option pricing, optimal portfolio investment, and interest rate models. Also included are simulations of stochastic phenomena, numerical solutions of the Black?Scholes?Merton equation, Monte Carlo methods, and time series. Basic measure theory is used as a tool to describe probabilistic phenomena. The level of familiarity with computer programming is kept to a minimum. To make the book accessible to a wider audience, some background mathematical facts are included in the first part of the book and also in the appendices. This work attempts to bridge the gap between mathematics and finance by using diagrams, graphs and simulations in addition to rigorous theoretical exposition. Simulations are not only used as the computational method in quantitative finance, but they can also facilitate an intuitive and deeper understanding of theoretical concepts. Stochastic Analysis for Finance with Simulations is designed for readers who want to have a deeper understanding of the delicate theory of quantitative finance by doing computer simulations in addition to theoretical study. It will particularly appeal to advanced undergraduate and graduate students in mathematics and business, but not excluding practitioners in finance industry. . 410 0$aUniversitext,$x0172-5939 606 $aMathematics 606 $aEconomics, Mathematical 606 $aMathematics, general$3https://scigraph.springernature.com/ontologies/product-market-codes/M00009 606 $aQuantitative Finance$3https://scigraph.springernature.com/ontologies/product-market-codes/M13062 615 0$aMathematics. 615 0$aEconomics, Mathematical. 615 14$aMathematics, general. 615 24$aQuantitative Finance. 676 $a519.22 700 $aChoe$b Geon Ho$4aut$4http://id.loc.gov/vocabulary/relators/aut$0756087 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910254063503321 996 $aStochastic analysis for finance with simulations$91523650 997 $aUNINA