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Stochastic Calculus for Finance evolved from the first ten years of the Carnegie Mellon Professional Master's program in Computational Finance. The content of this book has been used successfully with students whose mathematics background consists of calculus and calculus-based probability. The text gives both precise statements of results, plausibility arguments, and even some proofs, but more importantly intuitive explanations developed and refine through classroom experience with this material are provided. The book includes a self-contained treatment of the probability theory needed for stchastic calculus, including Brownian motion and its properties. Advanced topics include foreign exchange models, forward measures, and jump-diffusion processes. This book is being published in two volumes. The first volume presents the binomial asset-pricing model primarily as a vehicle for introducing in the simple setting the concepts needed for the continuous-time theory in the second volume. Chapter summaries and detailed illustrations are included. Classroom tested exercises conclude every chapter. Some of these extend the theory and others are drawn from practical problems in quantitative finance. Advanced undergraduates and Masters level students in mathematical finance and financial engineering will find this book useful. Steven E. Shreve is Co-Founder of the Carnegie Mellon MS Program in Computational Finance and winner of the Carnegie Mellon Doherty Prize for sustained contributions to education.

-332.0151922 --- 519.86 --- 336.7 --- AA / International- internationaal --- 305.970 --- 305.91 --- 305.7 --- 336.7 Geldwezen. Kredietwezen. Bankwezen. Financien. Monetaire econonomie. Beurswezen --- Geldwezen. Kredietwezen. Bankwezen. Financien. Monetaire econonomie. Beurswezen --- 519.86 Theory of economic-mathematical models --- Theory of economic-mathematical models --- Algemeenheden: Autoregression and moving average representation. ARIMA. ARMAX. Lagrange multiplier. Wald. Function (mis) specification. Autocorrelation. Homoscedasticity. Heteroscedasticity. ARCH. GARCH. Integration and co-integration. Unit roots. --- Econometrie van de financiële activa. Portfolio allocation en management. CAPM. Bubbles. --- Econometrie van het gedrag van de financiële tussenpersonen. Monetaire econometrische modellen. Monetaire agregaten. vraag voor geld. Krediet. Rente. --- Stochastic processes --- Finance --- Stochastic analysis --- Analysis, Stochastic --- Mathematical analysis --- Funding --- Funds --- Economics --- Currency question --- Mathematical models --- Econometrie van het gedrag van de financiële tussenpersonen. Monetaire econometrische modellen. Monetaire agregaten. vraag voor geld. Krediet. Rente --- Econometrie van de financiële activa. Portfolio allocation en management. CAPM. Bubbles --- Algemeenheden: Autoregression and moving average representation. ARIMA. ARMAX. Lagrange multiplier. Wald. Function (mis) specification. Autocorrelation. Homoscedasticity. Heteroscedasticity. ARCH. GARCH. Integration and co-integration. Unit roots --- Finances --- Analyse stochastique --- Textbooks --- Modèles mathématiques --- Manuels --- Textbooks. --- Economics, Mathematical . --- Applied mathematics. --- Engineering mathematics. --- Finance. --- Probabilities. --- Quantitative Finance. --- Applications of Mathematics. --- Finance, general. --- Probability Theory and Stochastic Processes. --- Probability --- Statistical inference --- Combinations --- Mathematics --- Chance --- Least squares --- Mathematical statistics --- Risk --- Engineering --- Engineering analysis --- Mathematical economics --- Econometrics --- Methodology --- Finance - Mathematical models - Textbooks --- Stochastic analysis - Textbooks --- Mathématique appliquée --- Probabilités --- Théorie financière

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Stochastic processes --- Brownian motion processes --- Stochastic analysis --- Mouvement brownien, Processus de --- Analyse stochastique

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This monograph is a sequel to Brownian Motion and Stochastic Calculus by the same authors. Within the context of Brownian-motion-driven asset prices, it develops contingent claim pricing and optimal consumption/investment in both complete and incomplete markets. The latter topic is extended to the study of complete market equilibrium, providing conditions for the existence and uniqueness of market prices which support trading by several heterogeneous agents. Although much of the incomplete-market material is available in research papers, these topics are treated for the first time in a unified manner. The book contains an extensive set of references and notes describing the field, including topics not treated in the text. This monograph should be of interest to researchers wishing to see advanced mathematics applied to finance. The material on optimal consumption and investment, leading to equilibrium, is addressed to the theoretical finance community. The chapters on contingent claim valuation present techniques of practical importance, especially for pricing exotic options. Also available by Ioannis Karatzas and Steven E. Shreve, Brownian Motion and Stochastic Calculus, Second Edition, Springer-Verlag New York, Inc., 1991, 470 pp., ISBN 0-387- 97655-8. .

Finance --- Brownian motion processes --- Business mathematics --- Contingent valuation --- Mathematical models --- Brownian motion processes. --- Business mathematics. --- Contingent valuation. --- Mathematical models. --- Stochastic processes --- 519.86 --- 336.7 --- -#ECO:02.01:financiële sector algemeen --- #ECO:01.02:economie theorie geschiedenis denken --- -Brownian motion processes --- 332.015195 --- 650.01513 --- Valuation --- Wiener processes --- Brownian movements --- Fluctuations (Physics) --- Markov processes --- Funding --- Funds --- Economics --- Currency question --- Arithmetic, Commercial --- Business --- Business arithmetic --- Business math --- Commercial arithmetic --- Mathematics --- 336.7 Geldwezen. Kredietwezen. Bankwezen. Financien. Monetaire econonomie. Beurswezen --- Geldwezen. Kredietwezen. Bankwezen. Financien. Monetaire econonomie. Beurswezen --- 519.86 Theory of economic-mathematical models --- Theory of economic-mathematical models --- Mathématiques financières --- Finances --- Mouvement brownien, Processus de --- Evaluation contingente --- Modèles mathématiques --- EPUB-LIV-FT SPRINGER-B --- Mathematics. --- Economics, Mathematical. --- Probabilities. --- Economic theory. --- Quantitative Finance. --- Probability Theory and Stochastic Processes. --- Economic Theory/Quantitative Economics/Mathematical Methods. --- Finance - Mathematical models --- -Business mathematics

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Stochastic optimal control : the discrete time case

Dynamic programming. --- Stochastic processes. --- Measure theory. --- Programmation dynamique --- Processus stochastiques --- Mesure, Théorie de la --- Dynamic programming --- Stochastic processes --- Measure theory --- Operations Research --- Civil & Environmental Engineering --- Engineering & Applied Sciences --- Lebesgue measure --- Measurable sets --- Measure of a set --- Algebraic topology --- Integrals, Generalized --- Measure algebras --- Rings (Algebra) --- Random processes --- Probabilities --- Mathematical optimization --- Programming (Mathematics) --- Systems engineering

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