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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.