{"product_id":"measure-probability-and-mathematical-finance-isbn-9781118831960","title":"Measure, Probability, and Mathematical Finance","description":"\u003cp\u003e\u003cb\u003eAn introduction to the mathematical theory and financial models developed and used on Wall Street\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eProviding both a theoretical and practical approach to the underlying mathematical theory behind financial models, \u003ci\u003eMeasure, Probability, and Mathematical Finance: A Problem-Oriented Approach\u003c\/i\u003e presents important concepts and results in measure theory, probability theory, stochastic processes, and stochastic calculus. Measure theory is indispensable to the rigorous development of probability theory and is also necessary to properly address martingale measures, the change of numeraire theory, and LIBOR market models. In addition, probability theory is presented to facilitate the development of stochastic processes, including martingales and Brownian motions, while stochastic processes and stochastic calculus are discussed to model asset prices and develop derivative pricing models.\u003c\/p\u003e \u003cp\u003eThe authors promote a problem-solving approach when applying mathematics in real-world situations, and readers are encouraged to address theorems and problems with mathematical rigor. In addition, \u003ci\u003eMeasure, Probability, and Mathematical Finance\u003c\/i\u003e features:\u003c\/p\u003e \u003cul\u003e \u003cli\u003eA comprehensive list of concepts and theorems from measure theory, probability theory, stochastic processes, and stochastic calculus\u003c\/li\u003e \u003cli\u003eOver 500 problems with hints and select solutions to reinforce basic concepts and important theorems\u003c\/li\u003e \u003cli\u003eClassic derivative pricing models in mathematical finance that have been developed and published since the seminal work of Black and Scholes\u003ci\u003e \u003c\/i\u003e\n\u003c\/li\u003e \u003c\/ul\u003e \u003ci\u003eMeasure, Probability, and Mathematical Finance: A Problem-Oriented Approach\u003c\/i\u003e is an ideal textbook for introductory quantitative courses in business, economics, and mathematical finance at the upper-undergraduate and graduate levels. The book is also a useful reference for readers who need to build their mathematical skills in order to better understand the mathematical theory of derivative pricing models.  \u003cp\u003ePreface xvii\u003c\/p\u003e \u003cp\u003eFinancial Glossary xxii\u003c\/p\u003e \u003cp\u003e\u003cb\u003ePart I Measure Theory\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e1 Sets and Sequences 3\u003c\/p\u003e \u003cp\u003e2 Measures 15\u003c\/p\u003e \u003cp\u003e3 Extension of Measures 29\u003c\/p\u003e \u003cp\u003e4 Lebesgue-Stieltjes Measures 37\u003c\/p\u003e \u003cp\u003e5 Measurable Functions 47\u003c\/p\u003e \u003cp\u003e6 Lebesgue Integration 57\u003c\/p\u003e \u003cp\u003e7 The Radon-Nikodym Theorem 77\u003c\/p\u003e \u003cp\u003e8 L\u003csup\u003eP\u003c\/sup\u003e Spaces 85\u003c\/p\u003e \u003cp\u003e9 Convergence 97\u003c\/p\u003e \u003cp\u003e10 Product Measures 113\u003c\/p\u003e \u003cp\u003e\u003cb\u003ePart II Probability Theory\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e11 Events and Random Variables 127\u003c\/p\u003e \u003cp\u003e12 Independence 141\u003c\/p\u003e \u003cp\u003e13 Expectation 161\u003c\/p\u003e \u003cp\u003e14 Conditional Expectation 173\u003c\/p\u003e \u003cp\u003e15 Inequalities 189\u003c\/p\u003e \u003cp\u003e16 Law of Large Numbers 199\u003c\/p\u003e \u003cp\u003e17 Characteristic Functions 217\u003c\/p\u003e \u003cp\u003e18 Discrete Distributions 227\u003c\/p\u003e \u003cp\u003e19 Continuous Distributions 239\u003c\/p\u003e \u003cp\u003e20 Central Limit Theorems 257\u003c\/p\u003e \u003cp\u003e\u003cb\u003ePart III Stochastic Processes\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e21 Stochastic Processes 271\u003c\/p\u003e \u003cp\u003e22 Martingales 291\u003c\/p\u003e \u003cp\u003e23 Stopping Times 301\u003c\/p\u003e \u003cp\u003e24 Martingale Inequalities 321\u003c\/p\u003e \u003cp\u003e25 Martingale Convergence Theorems 333\u003c\/p\u003e \u003cp\u003e26 Random Walks 343\u003c\/p\u003e \u003cp\u003e27 Poisson Processes 357\u003c\/p\u003e \u003cp\u003e28 Brownian Motion 373\u003c\/p\u003e \u003cp\u003e29 Markov Processes 389\u003c\/p\u003e \u003cp\u003e30 Lévy Processes 401\u003c\/p\u003e \u003cp\u003e\u003cb\u003ePart IV Stochastic Calculus\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e31 The Wiener Integral 421\u003c\/p\u003e \u003cp\u003e32 The Itô Integral 431\u003c\/p\u003e \u003cp\u003e33 Extension of the Itô Integral 453\u003c\/p\u003e \u003cp\u003e34 Martingale Stochastic Integrals 463\u003c\/p\u003e \u003cp\u003e35 The Itô Formula 477\u003c\/p\u003e \u003cp\u003e36 Martingale Representation Theorem 495\u003c\/p\u003e \u003cp\u003e37 Change of Measure 503\u003c\/p\u003e \u003cp\u003e38 Stochastic Differential Equations 515\u003c\/p\u003e \u003cp\u003e39 Diffusion 531\u003c\/p\u003e \u003cp\u003e40 The Feynman-Kac Formula 547\u003c\/p\u003e \u003cp\u003e\u003cb\u003ePart V Stochastic Financial Models\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e41 Discrete-Time Models 561\u003c\/p\u003e \u003cp\u003e42 Black-Scholes Option Pricing Models 579\u003c\/p\u003e \u003cp\u003e43 Path-Dependent Options 593\u003c\/p\u003e \u003cp\u003e44 American Options 609\u003c\/p\u003e \u003cp\u003e45 Short Rate Models 629\u003c\/p\u003e \u003cp\u003e46 Instantaneous Forward Rate Models 647\u003c\/p\u003e \u003cp\u003e47 LIBOR Market Models 667\u003c\/p\u003e \u003cp\u003eReferences 687\u003c\/p\u003e \u003cp\u003eList of Symbols 703\u003c\/p\u003e \u003cp\u003eSubject Index 707\u003c\/p\u003e  \u003cp\u003e\u003cb\u003eGUOJUN GAN, P\u003csmall\u003eH\u003c\/small\u003eD, ASA,\u003c\/b\u003e is Director of Quantitative Modeling and Model Efficiency at Manulife Financial, Canada. His research interests include empirical corporate finance, actuarial science, risk management, data mining, and big data analysis.\u003c\/p\u003e \u003cp\u003e\u003cb\u003eCHAOQUN MA, P\u003csmall\u003eH\u003c\/small\u003eD,\u003c\/b\u003e is Professor and Dean of the School of Business Administration at Hunan University, China. The recipient of First Prize in Outstanding Achievements in Teaching in 2009, Dr. Ma’s research interests include financial engineering, risk management, and data mining.\u003c\/p\u003e \u003cp\u003e\u003cb\u003eHONG XIE, P\u003csmall\u003eH\u003c\/small\u003eD,\u003c\/b\u003e is Adjunct Professor in the Department of Mathematics and Statistics at York University as well as Vice President of Models and Analytics at Manulife Financial, Canada. Dr. Xie is on the Board of Directors for the Canadian-Chinese Finance Association, and his research interests include financial engineering, mathematical finance, and partial differential equations.\u003c\/p\u003e  \u003cp\u003e\u003cb\u003eAn introduction to the mathematical theory and financial models developed and used on Wall Street\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eProviding both a theoretical and practical approach to the underlying mathematical theory behind financial models, \u003ci\u003eMeasure, Probability, and Mathematical Finance: A Problem-Oriented Approach\u003c\/i\u003e presents important concepts and results in measure theory, probability theory, stochastic processes, and stochastic calculus. Measure theory is indispensable to the rigorous development of probability theory and is also necessary to properly address martingale measures, the change of numeraire theory, and LIBOR market models. In addition, probability theory is presented to facilitate the development of stochastic processes, including martingales and Brownian motions, while stochastic processes and stochastic calculus are discussed to model asset prices and develop derivative pricing models.\u003c\/p\u003e \u003cp\u003eThe authors promote a problem-solving approach when applying mathematics in real-world situations, and readers are encouraged to address theorems and problems with mathematical rigor. In addition, \u003ci\u003eMeasure, Probability, and Mathematical Finance\u003c\/i\u003e features:\u003c\/p\u003e \u003cul\u003e \u003cli\u003eA comprehensive list of concepts and theorems from measure theory, probability theory, stochastic processes, and stochastic calculus\u003c\/li\u003e \u003cli\u003eOver 500 problems with hints and select solutions to reinforce basic concepts and important theorems\u003c\/li\u003e \u003cli\u003eClassic derivative pricing models in mathematical finance that have been developed and published since the seminal work of Black and Scholes\u003c\/li\u003e \u003c\/ul\u003e \u003cp\u003e\u003ci\u003eMeasure, Probability, and Mathematical Finance: A Problem-Oriented Approach\u003c\/i\u003e is an ideal textbook for introductory quantitative courses in business, economics, and mathematical finance at the upper-undergraduate and graduate levels. The book is also a useful reference for readers who need to build their mathematical skills in order to better understand the mathematical theory of derivative pricing models.\u003c\/p\u003e","brand":"Wiley","offers":[{"title":"Default Title","offer_id":47989592654053,"sku":"NP9781118831960","price":128.0,"currency_code":"USD","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/1842\/7735\/files\/9781118831960.jpg?v=1761784729","url":"https:\/\/k12savings.com\/products\/measure-probability-and-mathematical-finance-isbn-9781118831960","provider":"K12savings","version":"1.0","type":"link"}