Download or read book On a Multi dimensional Singular Stochastic Control Problem written by Nguyen Do Minh Nhat and published by . This book was released on 2015 with total page 104 pages. Available in PDF, EPUB and Kindle. Book excerpt: This dissertation considers a stochastic dynamic system which is governed by a multidimensional diffusion process with time dependent coefficients. The control acts additively on the state of the system. The objective is to minimize the expected cumulative cost associated with the position of the system and the amount of control exerted. It is proved that Hamilton-Jacobi-Bellman's equation of the problem has a solution, which corresponds to the optimal cost of the problem. We also investigate the smoothness of the free boundary arising from the problem. In the second part of the dissertation, we study the backward parabolic problem for a nonlinear parabolic equation of the form u_t + Au(t) = f (t, u(t)), u(T) = [phi], where A is a positive self-adjoint unbounded operator and f is a Lipschitz function. The problem is ill-posed, in the sense that if the solution does exist, it will not depend continuously on the data. To regularize the problem, we use the quasi-reversibility method to establish a modified problem. We present approximated solutions that depend on a small parameter [epsilon] > 0 and give error estimates for our regularization. These results extend some work on the nonlinear backward problem. Some numerical examples are given to justify the theoretical analysis.

Download or read book Singular and Bang Bang Stochastic Control written by and published by . This book was released on 1990 with total page 2 pages. Available in PDF, EPUB and Kindle. Book excerpt: Research supported by this grant focussed on the regularity of the value function for multi-dimensional singular stochastic control problems. In addition, a multi-dimensional finite-fuel problem has been studied, and known results for one dimensional problems have been extended to higher dimensions.

Download or read book Multi dimensional Finite fuel Singular Stochastic Control written by David S. Bridge and published by . This book was released on 1991 with total page 42 pages. Available in PDF, EPUB and Kindle. Book excerpt: Abstract: "A multi-dimensional Brownian motion is controlled so as to minimize the infinite-horizon, integrated, discounted second moment. The control process is singularly continuous, pushing the Brownian motion directly toward the origin whenever its norm reaches a certain critical level. The total amount of pushing which can be exerted over the infinite horizon is finite, and so as the remaining 'fuel' diminishes, the critical level at which control is exerted increases, but not to infinity. The optimal control eventually consumes all available fuel, and thereafter the Brownian motion is uncontrolled. The problem is solved by analysis of the associated Hamilton-Jacobi-Bellman variational inequality. The value function is found to be twice continuously differentiable, even across the free boundary associated with this variational inequality."

Download or read book A Free Boundary Problem Related to Singular Stochastic Control written by H. Mete Soner and published by . This book was released on 1990 with total page 22 pages. Available in PDF, EPUB and Kindle. Book excerpt: Abstract: "It is desired to control a multi-dimensional Brownian motion by adding a (possibly singularly) continuous process to its n[superscript th] components so as to minimize an expected infinite-horizon discounted running cost. The Hamilton-Jacobi-Bellman characterization of the value function is a variational inequality which has a unique twice continuously differentiable solution. The optimal process is constructed by solving the Skorokhod problem of reflecting the Brownian motion along a free boundary in the (0,0 ..., -1) direction."

Download or read book On Some Two Dimensional Singular Stochastic Control Problems and Their Free Boundary Analysis written by Patrick Schuhmann and published by . This book was released on 2021 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Regularity of the Value Function for a Two dimensional Singular Stochastic Control Problem written by H. Mete Soner and published by . This book was released on 1988 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Multidimensional Singular Control and Related Skorokhod Problem written by Jodi Dianetti and published by . This book was released on 2021 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: We characterize the optimal control for a class of singular stochastic control problems as the unique solution to a related Skorokhod reflection problem. The considered optimization problems concern the minimization of a discounted cost functional over an infinite time-horizon through a process of bounded variation affecting an Itˆo-diffusion. The setting is multidimensional, the dynamics of the state and the costs are convex, the volatility matrix can be constant or linear in the state. We prove that the optimal control acts only when the underlying diffusion attempts to exit the so-called waiting region, and that the direction of this action is prescribed by the derivative of the value function. Our approach is based on the study of a suitable monotonicity property of the derivative of the value function through its interpretation as the value of an optimal stopping game. Such a monotonicity allows to construct nearly optimal policies which reflect the underlying diffusion at the boundary of approximating waiting regions. The limit of this approximation scheme then provides the desired characterization. Our result applies to a relevant class of linear-quadratic models, among others. Furthermore, it allows to construct the optimal control in degenerate and non degenerate settings considered in the literature, where this important aspect was only partially addressed.

Download or read book A Solvable Two dimensional Degenerate Singular Stochastic Control Problem with Non Convex Costs written by Tiziano De Angelis and published by . This book was released on 2014 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: In this paper we provide a complete theoretical analysis of a two-dimensional degenerate non convex singular stochastic control problem. The optimisation is motivated by a storage-consumption model in an electricity market, and features a stochastic real-valued spot price modelled by Brownian motion. We find analytical expressions for the value function, the optimal control and the boundaries of the action and inaction regions. The optimal policy is characterised in terms of two monotone and discontinuous repelling free boundaries, although part of one boundary is constant and and the smooth fit condition holds there.

Download or read book Numerical Methods for Stochastic Control Problems in Continuous Time written by Harold Kushner and published by Springer Science & Business Media. This book was released on 2013-11-27 with total page 480 pages. Available in PDF, EPUB and Kindle. Book excerpt: Stochastic control is a very active area of research. This monograph, written by two leading authorities in the field, has been updated to reflect the latest developments. It covers effective numerical methods for stochastic control problems in continuous time on two levels, that of practice and that of mathematical development. It is broadly accessible for graduate students and researchers.

Download or read book Stochastic Optimal Control in Infinite Dimension written by Giorgio Fabbri and published by Springer. This book was released on 2017-06-22 with total page 928 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book Stochastic Control Problems for Multidimensional Martingales written by Benjamin A. Robinson and published by . This book was released on 2020 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book On a Class of Infinite dimensional Singular Stochastic Control Problems written by Salvatore Federico and published by . This book was released on 2019 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: We study a class of infinite-dimensional singular stochastic control problems with applications in economic theory and finance. The control process linearly affects an abstract evolution equation on a suitable partially-ordered infinite-dimensional space X, it takes values in the positive cone of X, and it has right-continuous and nondecreasing paths. We first provide a rigorous formulation of the problem by properly defining the controlled dynamics and integrals with respect to the control process. We then exploit the concave structure of our problem and derive necessary and sufficient first-order conditions for optimality. The latter are finally exploited in a specification of the model where we find an explicit expression of the optimal control. The techniques used are those of semigroup theory, vector-valued integration, convex analysis, and general theory of stochastic processes.

Download or read book On the Optimalboundary of a Three dimensional Singular Stochastic Control Problem Arising in Irreversible Investment written by Tiziano De Angelis and published by . This book was released on 2014 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Topics on Singular Stochastic Control and Related Stochastic Differential Equations written by Jin Ma and published by . This book was released on 1992 with total page 230 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Nonlinear Filtering of Partially Observed Systems Arising in Singular Stochastic Optimal Control written by Alessandro Calvia and published by . This book was released on 2021 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: This paper deals with a nonlinear filtering problem in which a multi-dimensional signal process is additively affected by a process v whose components have paths of bounded variation. The presence of the process v prevents from directly applying classical results and novel estimates need to be derived. By making use of the so-called reference probability measure approach, we derive the Zakai equation satisfied by the unnormalized filtering process, and then we deduce the corresponding Kushner-Stratonovich equation. Under the condition that the jump times of the process v do not accumulate over the considered time horizon, we show that the unnormalized filtering process is the unique solution to the Zakai equation, in the class of measure-valued processes having a square-integrable density. Our analysis paves the way to the study of stochastic control problems where a decision maker can exert singular controls in order to adjust the dynamics of an unobservable Itô-process.

Download or read book Applied Stochastic Control of Jump Diffusions written by Bernt Øksendal and published by Springer Science & Business Media. This book was released on 2007-04-26 with total page 263 pages. Available in PDF, EPUB and Kindle. Book excerpt: Here is a rigorous introduction to the most important and useful solution methods of various types of stochastic control problems for jump diffusions and its applications. Discussion includes the dynamic programming method and the maximum principle method, and their relationship. The text emphasises real-world applications, primarily in finance. Results are illustrated by examples, with end-of-chapter exercises including complete solutions. The 2nd edition adds a chapter on optimal control of stochastic partial differential equations driven by Lévy processes, and a new section on optimal stopping with delayed information. Basic knowledge of stochastic analysis, measure theory and partial differential equations is assumed.

Download or read book The Dynkin Festschrift written by Mark I. Freidlin and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 433 pages. Available in PDF, EPUB and Kindle. Book excerpt: Onishchik, A. A. Kirillov, and E. B. Vinberg, who obtained their first results on Lie groups in Dynkin's seminar. At a later stage, the work of the seminar was greatly enriched by the active participation of 1. 1. Pyatetskii Shapiro. As already noted, Dynkin started to work in probability as far back as his undergraduate studies. In fact, his first published paper deals with a problem arising in Markov chain theory. The most significant among his earliest probabilistic results concern sufficient statistics. In [15] and [17], Dynkin described all families of one-dimensional probability distributions admitting non-trivial sufficient statistics. These papers have considerably influenced the subsequent research in this field. But Dynkin's most famous results in probability concern the theory of Markov processes. Following Kolmogorov, Feller, Doob and Ito, Dynkin opened a new chapter in the theory of Markov processes. He created the fundamental concept of a Markov process as a family of measures corresponding to var ious initial times and states and he defined time homogeneous processes in terms of the shift operators ()t. In a joint paper with his student A.