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Stochastic processes --- Stochastic differential equations

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The main purpose of the book is to give a rigorous, yet mostly nontechnical, introduction to the most important and useful solution methods of various types of stochastic control problems for jump diffusions (i.e. solutions of stochastic differential equations driven by Lévy processes) and its applications. The types of control problems covered include classical stochastic control, optimal stopping, impulse control and singular control. Both the dynamic programming method and the maximum principle method are discussed, as well as the relation between them. Corresponding verification theorems involving the Hamilton-Jacobi Bellman equation and/or (quasi-)variational inequalities are formulated. There are also chapters on the viscosity solution formulation and numerical methods. The text emphasises applications, mostly to finance. All the main results are illustrated by examples and exercises appear at the end of each chapter with complete solutions. This will help the reader understand the theory and see how to apply it. The book assumes some basic knowledge of stochastic analysis, measure theory and partial differential equations.

Stochastic control theory --- Commande stochastique --- Stochastic control theory. --- Stochastic processes --- Viscosity solutions --- Operations Research --- Civil & Environmental Engineering --- Engineering & Applied Sciences --- Stochastic processes. --- Viscosity solutions. --- EPUB-LIV-FT LIVMATHE SPRINGER-B --- Random processes --- Mathematics. --- Operator theory. --- Economics, Mathematical. --- Operations research. --- Management science. --- Probabilities. --- Probability Theory and Stochastic Processes. --- Operations Research, Management Science. --- Operator Theory. --- Quantitative Finance. --- Hamilton-Jacobi equations --- Probabilities --- Control theory --- Distribution (Probability theory. --- Finance. --- Funding --- Funds --- Economics --- Currency question --- Functional analysis --- Distribution functions --- Frequency distribution --- Characteristic functions --- Economics, Mathematical . --- Mathematical economics --- Econometrics --- Mathematics --- Quantitative business analysis --- Management --- Problem solving --- Operations research --- Statistical decision --- Operational analysis --- Operational research --- Industrial engineering --- Management science --- Research --- System theory --- Probability --- Statistical inference --- Combinations --- Chance --- Least squares --- Mathematical statistics --- Risk --- Methodology

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Stochastic differential equations. --- 519.216 --- 517.9 --- Stochastic differential equations --- 681.3*H35 --- 681.3*H1 --- 681.3*H1 Models and principles (Information systems) --- Models and principles (Information systems) --- 681.3*H35 On-line information services: data bank sharing --- On-line information services: data bank sharing --- 517.9 Differential equations. Integral equations. Other functional equations. Finite differences. Calculus of variations. Functional analysis --- Differential equations. Integral equations. Other functional equations. Finite differences. Calculus of variations. Functional analysis --- 519.216 Stochastic processes in general. Prediction theory. Stopping times. Martingales --- Stochastic processes in general. Prediction theory. Stopping times. Martingales --- 519.2 --- Differential equations --- Fokker-Planck equation --- Mathematical analysis. --- Analysis (Mathematics). --- Probabilities. --- Mathematical physics. --- System theory. --- Calculus of variations. --- Partial differential equations. --- Analysis. --- Probability Theory and Stochastic Processes. --- Theoretical, Mathematical and Computational Physics. --- Systems Theory, Control. --- Calculus of Variations and Optimal Control; Optimization. --- Partial Differential Equations. --- Partial differential equations --- Isoperimetrical problems --- Variations, Calculus of --- Maxima and minima --- Systems, Theory of --- Systems science --- Science --- Physical mathematics --- Physics --- Probability --- Statistical inference --- Combinations --- Mathematics --- Chance --- Least squares --- Mathematical statistics --- Risk --- 517.1 Mathematical analysis --- Mathematical analysis --- Philosophy --- Physics. --- Mathematics. --- System theory --- Math --- Natural philosophy --- Philosophy, Natural --- Physical sciences --- Dynamics

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The main purpose of the book is to give a rigorous introduction to the most important and useful solution methods of various types of stochastic control problems for jump diffusions and their applications. Both the dynamic programming method and the stochastic maximum principle method are discussed, as well as the relation between them. Corresponding verification theorems involving the Hamilton–Jacobi–Bellman equation and/or (quasi-)variational inequalities are formulated. The text emphasises applications, mostly to finance. All the main results are illustrated by examples and exercises appear at the end of each chapter with complete solutions. This will help the reader understand the theory and see how to apply it. The book assumes some basic knowledge of stochastic analysis, measure theory and partial differential equations. The 3rd edition is an expanded and updated version of the 2nd edition, containing recent developments within stochastic control and its applications. Specifically, there is a new chapter devoted to a comprehensive presentation of financial markets modelled by jump diffusions, and one on backward stochastic differential equations and convex risk measures. Moreover, the authors have expanded the optimal stopping and the stochastic control chapters to include optimal control of mean-field systems and stochastic differential games.

Distribution (Probability theory. --- Finance. --- Mathematical optimization. --- Operator theory. --- Systems theory. --- Operations Research, Management Science. --- Probability Theory and Stochastic Processes. --- Quantitative Finance. --- Calculus of Variations and Optimal Control; Optimization. --- Operator Theory. --- Systems Theory, Control. --- Functional analysis --- Optimization (Mathematics) --- Optimization techniques --- Optimization theory --- Systems optimization --- Mathematical analysis --- Maxima and minima --- Operations research --- Simulation methods --- System analysis --- Funding --- Funds --- Economics --- Currency question --- Distribution functions --- Frequency distribution --- Characteristic functions --- Probabilities --- Stochastic processes. --- Dissemination process. --- Random processes --- Operations research. --- Management science. --- Probabilities. --- Economics, Mathematical . --- Calculus of variations. --- System theory. --- Systems, Theory of --- Systems science --- Science --- Isoperimetrical problems --- Variations, Calculus of --- Mathematical economics --- Econometrics --- Mathematics --- Probability --- Statistical inference --- Combinations --- Chance --- Least squares --- Mathematical statistics --- Risk --- Quantitative business analysis --- Management --- Problem solving --- Statistical decision --- Operational analysis --- Operational research --- Industrial engineering --- Management science --- Research --- System theory --- Philosophy --- Methodology --- Economics, Mathematical.

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The main purpose of the book is to give a rigorous, yet mostly nontechnical, introduction to the most important and useful solution methods of various types of stochastic control problems for jump diffusions and its applications. The types of control problems covered include classical stochastic control, optimal stopping, impulse control and singular control. Both the dynamic programming method and the maximum principle method are discussed, as well as the relation between them. Corresponding verification theorems involving the Hamilton-Jacobi Bellman equation and/or (quasi-)variational inequalities are formulated. There are also chapters on the viscosity solution formulation and numerical methods. The text emphasises applications, mostly to finance. All the main results are illustrated by examples and exercises appear at the end of each chapter with complete solutions. This will help the reader understand the theory and see how to apply it. The book assumes some basic knowledge of stochastic analysis, measure theory and partial differential equations. In the 2nd edition there is a new chapter on optimal control of stochastic partial differential equations driven by Lévy processes. There is also a new section on optimal stopping with delayed information. Moreover, corrections and other improvements have been made.

Quantitative methods (economics) --- Operator theory --- Operational research. Game theory --- Financial analysis --- analyse (wiskunde) --- stochastische analyse --- speltheorie --- financiële analyse --- operationeel onderzoek --- kansrekening