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Yielding new insights into important market phenomena like asset price bubbles and trading constraints, this is the first textbook to present asset pricing theory using the martingale approach (and all of its extensions). Since the 1970s asset pricing theory has been studied, refined, and extended, and many different approaches can be used to present this material. Existing PhD–level books on this topic are aimed at either economics and business school students or mathematics students. While the first mostly ignore much of the research done in mathematical finance, the second emphasizes mathematical finance but does not focus on the topics of most relevance to economics and business school students. These topics are derivatives pricing and hedging (the Black–Scholes–Merton, the Heath–Jarrow–Morton, and the reduced-form credit risk models), multiple-factor models, characterizing systematic risk, portfolio optimization, market efficiency, and equilibrium (capital asset and consumption) pricing models. This book fills this gap, presenting the relevant topics from mathematical finance, but aimed at Economics and Business School students with strong mathematical backgrounds. .

Mathematics. --- Economics, Mathematical. --- Mathematical optimization. --- Probabilities. --- Quantitative Finance. --- Probability Theory and Stochastic Processes. --- Optimization. --- Financial Mathematics. --- Finance. --- Distribution (Probability theory. --- Finance—Mathematics. --- Distribution functions --- Frequency distribution --- Characteristic functions --- Probabilities --- Funding --- Funds --- Economics --- Currency question --- Optimization (Mathematics) --- Optimization techniques --- Optimization theory --- Systems optimization --- Mathematical analysis --- Maxima and minima --- Operations research --- Simulation methods --- System analysis --- Martingales (Mathematics) --- Pricing. --- Economics, Mathematical . --- Probability --- Statistical inference --- Combinations --- Mathematics --- Chance --- Least squares --- Mathematical statistics --- Risk --- Mathematical economics --- Econometrics --- Methodology

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This book describes five qualitative investment decision-making methods based on the hesitant fuzzy information. They are: (1) the investment decision-making method based on the asymmetric hesitant fuzzy sigmoid preference relations, (2) the investment decision-making method based on the hesitant fuzzy trade-off and portfolio selection, (3) the investment decision-making method based on the hesitant fuzzy preference envelopment analysis, (4) the investment decision-making method based on the hesitant fuzzy peer-evaluation and strategy fusion, and (5) the investment decision-making method based on the EHVaR measurement and tail analysis.

Engineering. --- Financial engineering. --- Operations research. --- Finance—Mathematics. --- Computational Intelligence. --- Financial Engineering. --- Operations Research/Decision Theory. --- Financial Mathematics. --- Operational analysis --- Operational research --- Industrial engineering --- Management science --- Research --- System theory --- Computational finance --- Engineering, Financial --- Finance --- Construction --- Industrial arts --- Technology --- Fuzzy decision making. --- Decision making --- Fuzzy mathematics --- Computational intelligence. --- Decision making. --- Deciding --- Decision (Psychology) --- Decision analysis --- Decision processes --- Making decisions --- Management --- Management decisions --- Choice (Psychology) --- Problem solving --- Intelligence, Computational --- Artificial intelligence --- Soft computing

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Nonlinear theories --- System analysis --- Chaos --- Economics --- Finance --- Théories non linéaires --- Analyse de systèmes --- Chaos (Théorie des systèmes) --- Economie politique --- Finances --- Mathematical models --- Modèles mathématiques --- AA / International- internationaal --- 305.971 --- Speciale gevallen in econometrische modelbouw. --- Théories non linéaires --- Analyse de systèmes --- Chaos (Théorie des systèmes) --- Modèles mathématiques --- Financial Mathematics --- System analysis. --- Chaotic behavior in systems --- Economics, Mathematical --- Mathematical economics --- Econometrics --- Mathematics --- Nonlinear problems --- Nonlinearity (Mathematics) --- Calculus --- Mathematical analysis --- Mathematical physics --- Chaos in systems --- Chaos theory --- Chaotic motion in systems --- Differentiable dynamical systems --- Dynamics --- System theory --- Speciale gevallen in econometrische modelbouw --- Methodology --- THEORIE NON LINEAIRE --- ANALYSE DES SYSTEMES --- SYSTEMES DYNAMIQUES --- THEORIE DU CHAOS --- ECONOMIE POLITIQUE --- FINANCES --- MODELES MATHEMATIQUES

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This open access brief introduces the basic principles of control theory in a concise self-study guide. It complements the classic texts by emphasizing the simple conceptual unity of the subject. A novice can quickly see how and why the different parts fit together. The concepts build slowly and naturally one after another, until the reader soon has a view of the whole. Each concept is illustrated by detailed examples and graphics. The full software code for each example is available, providing the basis for experimenting with various assumptions, learning how to write programs for control analysis, and setting the stage for future research projects. The topics focus on robustness, design trade-offs, and optimality. Most of the book develops classical linear theory. The last part of the book considers robustness with respect to nonlinearity and explicitly nonlinear extensions, as well as advanced topics such as adaptive control and model predictive control. New students, as well as scientists from other backgrounds who want a concise and easy-to-grasp coverage of control theory, will benefit from the emphasis on concepts and broad understanding of the various approaches.

Engineering. --- System theory. --- Mathematical physics. --- Biomathematics. --- Control engineering. --- Control. --- Systems Theory, Control. --- Mathematical and Computational Biology. --- Mathematical Applications in the Physical Sciences. --- Financial Mathematics. --- Control engineering --- Control equipment --- Control theory --- Engineering instruments --- Automation --- Programmable controllers --- Biology --- Mathematics --- Physical mathematics --- Physics --- Systems, Theory of --- Systems science --- Science --- Construction --- Industrial arts --- Technology --- Philosophy --- Systems theory. --- Finance—Mathematics. --- Control and Systems Theory. --- Finance --- Mathematics. --- Arithmetic, Commercial --- Business --- Business arithmetic --- Business math --- Commercial arithmetic --- Itinerario de Automática (70884203) --- Bibliografía recomendada --- Control Theory --- Wolfram Mathematica Software --- Robust Control --- Engineering Design Tradeoffs --- Feedback Control Systems --- Optimal Control --- Control theory. --- Social sciences --- Systems Theory, Control . --- Mathematical Physics. --- Mathematics in Business, Economics and Finance. --- Dynamics --- Machine theory

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This monograph focuses on those stochastic quickest detection tasks in disorder problems that arise in the dynamical analysis of statistical data. These include quickest detection of randomly appearing targets, of spontaneously arising effects, and of arbitrage (in financial mathematics). There is also currently great interest in quickest detection methods for randomly occurring ‘intrusions’ in information systems and in the design of defense methods against cyber-attacks. The author shows that the majority of quickest detection problems can be reformulated as optimal stopping problems where the stopping time is the moment the occurrence of ‘disorder’ is signaled. Thus, considerable attention is devoted to the general theory of optimal stopping rules, and to its concrete problem-solving methods. The exposition covers both the discrete time case, which is in principle relatively simple and allows step-by-step considerations, and the continuous-time case, which often requires more technical machinery such as martingales, supermartingales, and stochastic integrals. There is a focus on the well-developed apparatus of Brownian motion, which enables the exact solution of many problems. The last chapter presents applications to financial markets. Researchers and graduate students interested in probability, decision theory and statistical sequential analysis will find this book useful.

Systems theory. --- Distribution (Probability theory. --- Mathematical statistics. --- Finance. --- Finance—Mathematics. --- Statistics. --- Systems Theory, Control. --- Probability Theory and Stochastic Processes. --- Statistical Theory and Methods. --- Quantitative Finance. --- Financial Mathematics. --- Bayesian Inference. --- Statistical analysis --- Statistical data --- Statistical methods --- Statistical science --- Mathematics --- Econometrics --- Funding --- Funds --- Economics --- Currency question --- Statistical inference --- Statistics, Mathematical --- Statistics --- Probabilities --- Sampling (Statistics) --- Distribution functions --- Frequency distribution --- Characteristic functions --- System theory. --- Probabilities. --- Statistics . --- Economics, Mathematical . --- Mathematical economics --- Probability --- Combinations --- Chance --- Least squares --- Mathematical statistics --- Risk --- Systems, Theory of --- Systems science --- Science --- Methodology --- Philosophy --- Control theory. --- Social sciences --- Systems Theory, Control . --- Probability Theory. --- Mathematics in Business, Economics and Finance. --- Mathematics. --- Dynamics --- Machine theory