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This book is intended for university seniors and graduate students majoring in probability theory or mathematical finance. In the first chapter, results in probability theory are reviewed. Then, it follows a discussion of discrete-time martingales, continuous time square integrable martingales (particularly, continuous martingales of continuous paths), stochastic integrations with respect to continuous local martingales, and stochastic differential equations driven by Brownian motions. In the final chapter, applications to mathematical finance are given. The preliminary knowledge needed by the reader is linear algebra and measure theory. Rigorous proofs are provided for theorems, propositions, and lemmas. In this book, the definition of conditional expectations is slightly different than what is usually found in other textbooks. For the Doob–Meyer decomposition theorem, only square integrable submartingales are considered, and only elementary facts of the square integrable functions are used in the proof. In stochastic differential equations, the Euler–Maruyama approximation is used mainly to prove the uniqueness of martingale problems and the smoothness of solutions of stochastic differential equations. .

Functional analysis --- Probability theory --- Mathematics --- Measuring methods in physics --- Applied physical engineering --- toegepaste wiskunde --- waarschijnlijkheidstheorie --- functies (wiskunde) --- economie --- meettechniek --- wiskunde

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A lot of economic problems can be formulated as constrained optimizations and equilibration of their solutions. Various mathematical theories have been supplying economists with indispensable machineries for these problems arising in economic theory. Conversely, mathematicians have been stimulated by various mathematical difficulties raised by economic theories. The series is designed to bring together those mathematicians who are seriously interested in getting new challenging stimuli from economic theories with those economists who are seeking effective mathematical tools for their research.

Economics, Mathematical. --- Economics --- Mathematical economics --- Econometrics --- Mathematics --- Methodology --- Mathematics. --- Distribution (Probability theory. --- Game Theory, Economics, Social and Behav. Sciences. --- Probability Theory and Stochastic Processes. --- Applications of Mathematics. --- Distribution functions --- Frequency distribution --- Characteristic functions --- Probabilities --- Math --- Science --- Game theory. --- Probabilities. --- Applied mathematics. --- Engineering mathematics. --- Engineering --- Engineering analysis --- Mathematical analysis --- Probability --- Statistical inference --- Combinations --- Chance --- Least squares --- Mathematical statistics --- Risk --- Games, Theory of --- Theory of games --- Mathematical models

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The series is designed to bring together those mathematicians who are seriously interested in getting new challenging stimuli from economic theories with those economists who are seeking effective mathematical tools for their research. A lot of economic problems can be formulated as constrained optimizations and equilibration of their solutions. Various mathematical theories have been supplying economists with indispensable machineries for these problems arising in economic theory. Conversely, mathematicians have been stimulated by various mathematical difficulties raised by economic theories.

Mathematics. --- Game Theory, Economics, Social and Behav. Sciences. --- Probability Theory and Stochastic Processes. --- Distribution (Probability theory). --- Mathématiques --- Distribution (Théorie des probabilités) --- Distribution (Probability theory. --- Business & Economics --- Mathematics --- Physical Sciences & Mathematics --- Algebra --- Economic Theory --- Economics, Mathematical. --- Economics --- Mathematical economics --- Game theory. --- Probabilities. --- Econometrics --- Methodology --- Distribution functions --- Frequency distribution --- Characteristic functions --- Probabilities --- Math --- Science --- Probability --- Statistical inference --- Combinations --- Chance --- Least squares --- Mathematical statistics --- Risk --- Games, Theory of --- Theory of games --- Mathematical models

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A lot of economic problems can be formulated as constrained optimizations and equilibration of their solutions. Various mathematical theories have been supplying economists with indispensable machineries for these problems arising in economic theory. Conversely, mathematicians have been stimulated by various mathematical difficulties raised by economic theories. The series is designed to bring together those mathematicians who are seriously interested in getting new challenging stimuli from economic theories with those economists who are seeking effective mathematical tools for their research.

Economics. --- Mathematics. --- Mathematics --- Business & Economics --- Physical Sciences & Mathematics --- Algebra --- Economic Theory --- Economics, Mathematical. --- Economics --- Mathematical economics --- Applied mathematics. --- Engineering mathematics. --- Game theory. --- Probabilities. --- Game Theory, Economics, Social and Behav. Sciences. --- Probability Theory and Stochastic Processes. --- Applications of Mathematics. --- Econometrics --- Methodology --- Distribution (Probability theory. --- Distribution functions --- Frequency distribution --- Characteristic functions --- Probabilities --- Math --- Science --- Engineering --- Engineering analysis --- Mathematical analysis --- Probability --- Statistical inference --- Combinations --- Chance --- Least squares --- Mathematical statistics --- Risk --- Games, Theory of --- Theory of games --- Mathematical models

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Advances in Mathematical Economics is a publication of the Research Center for Mathematical Economics, which was founded in 1997 as an international scientific association that aims to promote research activities in mathematical economics. Our publication was launched to realize our long-term goal of bringing together those mathematicians who are seriously interested in obtaining new challenging stimuli from economic theories and those economists who are seeking effective mathematical tools for their research. The scope of Advances in Mathematical Economics includes, but is not limited to, the following fields: - economic theories in various fields based on rigorous mathematical reasoning; - mathematical methods (e.g., analysis, algebra, geometry, probability) motivated by economic theories; - mathematical results of potential relevance to economic theory; - historical study of mathematical economics. Authors are asked to develop their original results as fully as possible and also to give a clear-cut expository overview of the problem under discussion. Consequently, we will also invite articles which might be considered too long for publication in journals.

Economics -- Mathematical models. --- Economics -- Methodology. --- Economics, Mathematical -- Periodicals. --- Economic Theory --- Business & Economics --- Economics, Mathematical --- -330.0151 --- Economics --- Mathematical economics --- Econometrics --- Mathematics --- Electronic information resources --- Methodology --- E-books --- AA / International- internationaal --- 305.970 --- 305.6 --- 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. --- Risicotheorie, speltheorie. Risicokapitaal. Beslissingsmodellen. --- Economics, Mathematical. --- Methodology. --- Economic theory. --- Economics. --- Economic Theory/Quantitative Economics/Mathematical Methods. --- Economic theory --- Political economy --- Social sciences --- Economic man --- 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 --- Risicotheorie, speltheorie. Risicokapitaal. Beslissingsmodellen