Optimal Stochastic Control, Stochastic Target Problems, and Backward SDE - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Optimal Stochastic Control, Stochastic Target Problems, and Backward SDE write by Nizar Touzi. This book was released on 2012-09-27. Optimal Stochastic Control, Stochastic Target Problems, and Backward SDE available in PDF, EPUB and Kindle. This book collects some recent developments in stochastic control theory with applications to financial mathematics. We first address standard stochastic control problems from the viewpoint of the recently developed weak dynamic programming principle. A special emphasis is put on the regularity issues and, in particular, on the behavior of the value function near the boundary. We then provide a quick review of the main tools from viscosity solutions which allow to overcome all regularity problems. We next address the class of stochastic target problems which extends in a nontrivial way the standard stochastic control problems. Here the theory of viscosity solutions plays a crucial role in the derivation of the dynamic programming equation as the infinitesimal counterpart of the corresponding geometric dynamic programming equation. The various developments of this theory have been stimulated by applications in finance and by relevant connections with geometric flows. Namely, the second order extension was motivated by illiquidity modeling, and the controlled loss version was introduced following the problem of quantile hedging. The third part specializes to an overview of Backward stochastic differential equations, and their extensions to the quadratic case.
Optimal Stochastic Control, Stochastic Target Problems, and Backward Sde
Optimal Stochastic Control, Stochastic Target Problems, and Backward Sde - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Optimal Stochastic Control, Stochastic Target Problems, and Backward Sde write by Springer. This book was released on 2012-09-01. Optimal Stochastic Control, Stochastic Target Problems, and Backward Sde available in PDF, EPUB and Kindle.
Optimal Stochastic Control, Stochastic Target Problems, and Backward SDE
Optimal Stochastic Control, Stochastic Target Problems, and Backward SDE - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Optimal Stochastic Control, Stochastic Target Problems, and Backward SDE write by Nizar Touzi. This book was released on 2012-09-25. Optimal Stochastic Control, Stochastic Target Problems, and Backward SDE available in PDF, EPUB and Kindle. This book collects some recent developments in stochastic control theory with applications to financial mathematics. We first address standard stochastic control problems from the viewpoint of the recently developed weak dynamic programming principle. A special emphasis is put on the regularity issues and, in particular, on the behavior of the value function near the boundary. We then provide a quick review of the main tools from viscosity solutions which allow to overcome all regularity problems. We next address the class of stochastic target problems which extends in a nontrivial way the standard stochastic control problems. Here the theory of viscosity solutions plays a crucial role in the derivation of the dynamic programming equation as the infinitesimal counterpart of the corresponding geometric dynamic programming equation. The various developments of this theory have been stimulated by applications in finance and by relevant connections with geometric flows. Namely, the second order extension was motivated by illiquidity modeling, and the controlled loss version was introduced following the problem of quantile hedging. The third part specializes to an overview of Backward stochastic differential equations, and their extensions to the quadratic case.
Stochastic Optimal Control in Infinite Dimension
Stochastic Optimal Control in Infinite Dimension - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Stochastic Optimal Control in Infinite Dimension write by Giorgio Fabbri. This book was released on 2017-06-22. Stochastic Optimal Control in Infinite Dimension available in PDF, EPUB and Kindle. Providing an introduction to stochastic optimal control in infinite dimension, this book gives a complete account of the theory of second-order HJB equations in infinite-dimensional Hilbert spaces, focusing on its applicability to associated stochastic optimal control problems. It features a general introduction to optimal stochastic control, including basic results (e.g. the dynamic programming principle) with proofs, and provides examples of applications. A complete and up-to-date exposition of the existing theory of viscosity solutions and regular solutions of second-order HJB equations in Hilbert spaces is given, together with an extensive survey of other methods, with a full bibliography. In particular, Chapter 6, written by M. Fuhrman and G. Tessitore, surveys the theory of regular solutions of HJB equations arising in infinite-dimensional stochastic control, via BSDEs. The book is of interest to both pure and applied researchers working in the control theory of stochastic PDEs, and in PDEs in infinite dimension. Readers from other fields who want to learn the basic theory will also find it useful. The prerequisites are: standard functional analysis, the theory of semigroups of operators and its use in the study of PDEs, some knowledge of the dynamic programming approach to stochastic optimal control problems in finite dimension, and the basics of stochastic analysis and stochastic equations in infinite-dimensional spaces.
Stochastic Linear-Quadratic Optimal Control Theory: Open-Loop and Closed-Loop Solutions
Stochastic Linear-Quadratic Optimal Control Theory: Open-Loop and Closed-Loop Solutions - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Stochastic Linear-Quadratic Optimal Control Theory: Open-Loop and Closed-Loop Solutions write by Jingrui Sun. This book was released on 2020-06-29. Stochastic Linear-Quadratic Optimal Control Theory: Open-Loop and Closed-Loop Solutions available in PDF, EPUB and Kindle. This book gathers the most essential results, including recent ones, on linear-quadratic optimal control problems, which represent an important aspect of stochastic control. It presents the results in the context of finite and infinite horizon problems, and discusses a number of new and interesting issues. Further, it precisely identifies, for the first time, the interconnections between three well-known, relevant issues – the existence of optimal controls, solvability of the optimality system, and solvability of the associated Riccati equation. Although the content is largely self-contained, readers should have a basic grasp of linear algebra, functional analysis and stochastic ordinary differential equations. The book is mainly intended for senior undergraduate and graduate students majoring in applied mathematics who are interested in stochastic control theory. However, it will also appeal to researchers in other related areas, such as engineering, management, finance/economics and the social sciences.
