Measure, Probability, and Mathematical Finance : A Problem-Oriented Approach

• Record Nr.: UNINA9910810312403321
• Autore: Gan Guojun
• Pubbl/distr/stampa: Somerset : , : John Wiley & Sons, Incorporated, , 2014; ©2014
• ISBN: 9781118831984; 9781118831960
• Edizione: [1st ed.]
• Descrizione fisica: 1 online resource (741 pages)
• Altri autori (Persone): MaChaoqun; XieHong
• Disciplina: 332.015195
• Soggetti: Finance -- Mathematical models; Finance -- Research; Social sciences -- Research -- Statistical methods
• Lingua di pubblicazione: Inglese
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Nota di contenuto: Intro -- MEASURE, PROBABILITY, AND MATHEMATICAL FINANCE: A Problem-Oriented Approach -- Copyright -- CONTENTS -- Preface -- Financial Glossary -- PART I MEASURE THEORY -- 1 Sets and Sequences -- 1.1 Basic Concepts and Facts -- 1.2 Problems -- 1.3 Hints -- 1.4 Solutions -- 1.5 Bibliographic Notes -- 2 MEASURES -- 2.1 Basic Concepts and Facts -- 2.2 Problems -- 2.3 Hints -- 2.4 Solutions -- 2.5 Bibliographic Notes -- 3 EXTENSION OF MEASURES -- 3.1 Basic Concepts and Facts -- 3.2 Problems -- 3.3 Hints -- 3.4 Solutions -- 3.5 Bibliographic Notes -- 4 LEBESGUE-STIELT JES MEASURES -- 4.1 Basic Concepts and Facts -- 4.2 Problems -- 4.3 Hints -- 4.4 Solutions -- 4.5 Bibliographic Notes -- 5 MEASURABLE FUNCTIONS -- 5.1 Basic Concepts and Facts -- 5.2 Problems -- 5.3 Hints -- 5.4 Solutions -- 5.5 Bibliographic Notes -- 6 LEBESGUE INTEGRATION -- 6.1 Basic Concepts and Facts -- 6.2 Problems -- 6.3 Hints -- 6.4 Solutions -- 6.5 Bibliographic Notes -- 7 THE RADON-NIKODYM THEOREM -- 7.1 Basic Concepts and Facts -- 7.2 Problems -- 7.3 Hints -- 7.4 Solutions -- 7.5 Bibliographic Notes -- 8 LP SPACES -- 8.1 Basic Concepts and Facts -- 8.2 Problems -- 8.3 Hints -- 8.4 Solutions -- 8.5 ; Bibliographic Notes -- 9 CONVERGENCE -- 9.1 Basic Concepts and Facts -- 9.2 Problems -- 9.3 Hints -- 9.4 Solutions -- 9.5 Bibliographic Notes -- 10 PRODUCT MEASURES -- 10.1 Basic Concepts and Facts -- 10.2 Problems -- 10.3 Hints -- 10.4 Solutions -- 10.5 Bibliographic Notes -- PART II PROBABILITY THEORY -- 11 EVENTS AND RANDOM VARIABLES -- 11.1 Basic Concepts and Facts -- 11.2 Problems -- 11.3 Hints -- 11.4 Solutions -- 11.5 Bibliographic Notes -- 12 INDEPENDENCE -- 12.1 Basic Concepts and Facts -- 12.2 Problems -- 12.3 Hints -- 12.4 Solutions -- 12.5 Bibliographic Notes -- 13 EXPECTATION -- 13.1 Basic Concepts and Facts -- 13.2 Problems -- 13.3 Hints -- 13.4 Solutions.; 13.5 Bibliographic Notes -- 14 CONDITIONAL EXPECTATION -- 14.1 Basic Concepts and Facts -- 14.2 Problems -- 14.3 Hints -- 14.4 Solutions -- 14.5 Bibliographic Notes -- 15 INEQUALITIES -- 15.1 Basic Concepts and Facts -- 15.2 Problems -- 15.3 Hints -- 15.4 Solutions -- 15.5 Bibliographic Notes -- 16 LAW OF LARGE NUMBERS -- 16.1 Basic Concepts and Facts -- 16.2 Problems -- 16.3 Hints -- 16.4 Solutions -- 16.5 Bibliographic Notes -- 17 CHARACTERISTIC FUNCTIONS -- 17.1 Basic Concepts and Facts -- 17.2 Problems -- 17.3 Hints -- 17.4 Solutions -- 17.5 Bibliographic Notes -- 18 DISCRETE DISTRIBUTIONS -- 18.1 Basic Concepts and Facts -- 18.2 Problems -- 18.3 Hints -- 18.4 Solutions -- 18.5 Bibliographic Notes -- 19 CONTINUOUS DISTRIBUTIONS -- 19.1 Basic Concepts and Facts -- 19.2 Problems -- 19.3 Hints -- 19.4 Solutions -- 19.5 Bibliographic Notes -- 20 CENTRAL LIMIT THEOREMS -- 20.1 Basic Concepts and Facts -- 20.2 Problems -- 20.3 Hints -- 20.4 Solutions -- 20.5 Bibliographic Notes -- PART III STOCHASTIC PROCESSES -- 21 STOCHASTIC PROCESSES -- 21.1 Basic Concepts and Facts -- 21.2 Problems -- 21.3 Hints -- 21.4 Solutions -- 21.5 Bibliographic Notes -- 22 MARTINGALES -- 22.1 Basic Concepts and Facts -- 22.2 Problems -- 22.3 Hints -- 22.4 Solutions -- 22.5 Bibliographic Notes -- 23 STOPPING TIMES -- 23.1 Basic Concepts and Facts -- 23.2 Problems -- 23.3 Hints -- 23.4 Solutions -- 23.5 Bibliographic Notes -- 24 MARTINGALE INEQUALITIES -- 24.1 Basic Concepts and Facts -- 24.2 Problems -- 24.3 Hints -- 24.4 Solutions -- 24.5 Bibliographic Notes -- 25 MARTINGALE CONVERGENCE THEOREMS -- 25.1 Basic Concepts and Facts -- 25.2 Problems -- 25.3 Hints -- 25.4 Solutions -- 25.5 Bibliographic Notes -- 26 RANDOM WALKS -- 26.1 Basic Concepts and Facts -- 26.2 Problems -- 26.3 Hints -- 26.4 Solutions -- 26.5 Bibliographic Notes -- 27 POISSON PROCESSES.; 27.1 Basic Concepts and Facts -- 27.2 Problems -- 27.3 Hints -- 27.4 Solutions -- 27.5 Bibliographic Notes -- 28 BROWNIAN MOTION -- 28.1 Basic Concepts and Facts -- 28.2 Problems -- 28.3 Hints -- 28.4 Solutions -- 28.5 Bibliographic Notes -- 29 MARKOV PROCESSES -- 29.1 Basic Concepts and Facts -- 29.2 Problems -- 29.3 Hints -- 29.4 Solutions -- 29.5 Bibliographic Notes -- 30 LEVY PROCESSES -- 30.1 Basic Concepts and Facts -- 30.2 Problems -- 30.3 Hints -- 30.4 Solutions -- 30.5 Bibliographic Notes -- PART IV STOCHASTIC CALCULUS -- 31THE WIENER INTEGRAL -- 31.1 Basic Concepts and Facts -- 31.2 Problems -- 31.3 Hints -- 31.4 Solutions -- 31.5 Bibliographic Notes -- 32 THE ITO INTEGRAL -- 32.1 Basic Concepts and Facts -- 32.2 Problems -- 32.3 Hints -- 32.4 Solutions -- 32.5 Bibliographic Notes -- 33 EXTENSION OF THE ITO INTEGRAL -- 33.1 Basic Concepts and Facts -- 33.2 Problems -- 33.3 Hints -- 33.4 Solutions -- 33.5 Bibliographic Notes -- 34 MARTINGALE STOCHASTIC INTEGRALS -- 34.1 Basic Concepts and Facts -- 34.2 Problems -- 34.3 Hints -- 34.4 Solutions -- 34.5 Bibliographic Notes -- 35 THE ITO FORMULA -- 35.1 Basic Concepts and Facts -- 35.2 Problems -- 35.3 ; Hints -- 35.4 Solutions -- 35.5 Bibliographic Notes -- 36 MARTINGALE REPRESENTATION THEOREM -- 36.1 Basic Concepts and Facts -- 36.2 Problems -- 36.3 Hints -- 36.4 Solutions -- 36.5 Bibliographic Notes -- 37 CHANGE OF MEASURE -- 37.1 Basic Concepts and Facts -- 37.2 Problems -- 37.3 Hints -- 37.4 Solutions -- 37.5 Bibliographic Notes -- 38 STOCHASTIC DIFFERENTIAL EQUATIONS -- 38.1 Basic Concepts and Facts -- 38.2 Problems -- 38.3 Hints -- 38.4 Solutions -- 38.5 Bibliographic Notes -- 39 DIFFUSION -- 39.1 Basic Concepts and Facts -- 39.2 Problems -- 39.3 Hints -- 39.4 Solutions -- 39.5 Bibliographic Notes -- 40 THE FEYNMAN-KAC FORMULA -- 40.1 Basic Concepts and Facts -- 40.2 Problems -- 40.3 Hints.; 40.4 Solutions -- 40.5 Bibliographic Notes -- PART V STOCHASTIC FINANCIAL MODELS -- 41 DISCRETE-TIME MODELS -- 41.1 Basic Concepts and Facts -- 41.2 Problems -- 41.3 Hints -- 41.4 Solutions -- 41.5 Bibliographic Notes -- 42 BLACK-SCHOLES OPTION PRICING MODELS -- 42.1 Basic Concepts and Facts -- 42.2 Problems -- 42.3 Hints -- 42.4 Solutions -- 42.5 Bibliographic Notes -- 43 PATH-DEPENDENT OPTIONS -- 43.1 Basic Concepts and Facts -- 43.2 Problems -- 43.3 Hints -- 43.4 Solutions -- 43.5 Bibliographic Notes -- 44 AMERICAN OPTIONS -- 44.1 Basic Concepts and Facts -- 44.2 Problems -- 44.3 Hints -- 44.4 Solutions -- 44.5 Bibliographic Notes -- 45 SHORT RATE MODELS -- 45.1 Basic Concepts and Facts -- 45.2 Problems -- 45.3 Hints -- 45.4 Solutions -- 45.5 Bibliographic Notes -- 46 INSTANTANEOUS FORWARD RATEMODELS -- 46.1 Basic Concepts and Facts -- 46.2 Problems -- 46.3 Hints -- 46.4 Solutions -- 46.5 Bibliographic Notes -- 47 LIBOR MARKET MODELS -- 47.1 Basic Concepts and Facts -- 47.2 Problems -- 47.3 Hints -- 47.4 Solutions -- 47.5 Bibliographic Notes -- References -- List of Symbols -- Subject Index.
• Sommario/riassunto: An introduction to the mathematical theory and financial models developed and used on Wall Street Providing both a theoretical and practical approach to the underlying mathematical theory behind financial models, Measure, Probability, and Mathematical Finance: A Problem-Oriented Approach 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. The 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, Measure, Probability, and Mathematical Finance features: A comprehensive list of concepts and theorems from measure theory, probability theory, stochastic processes, and stochastic calculus Over 500 problems with hints and select solutions to reinforce basic concepts and important theorems Classic derivative pricing models in mathematical finance that have been developed and published since the seminal work of Black and Scholes Measure, Probability, and Mathematical Finance: A Problem-Oriented Approach 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.