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 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 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 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 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 SIAM Journal on Control and Optimization written by Society for Industrial and Applied Mathematics and published by . This book was released on 2006 with total page 800 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Convex Duality for Finite fuel Problems in Singular Stochastic Control written by Hang Zhu and published by . This book was released on 1990 with total page 40 pages. Available in PDF, EPUB and Kindle. Book excerpt:
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 Scientific and Technical Aerospace Reports written by and published by . This book was released on 1995 with total page 702 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 Research in Progress written by and published by . This book was released on 1992 with total page 302 pages. Available in PDF, EPUB and Kindle. Book excerpt:
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 0 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 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 Impulse Control of Multidimensional Diffusion and Jump Diffusion Processes written by Guoliang Wu and published by . This book was released on 2009 with total page 220 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Mathematical Finance written by Michael Kohlmann and published by Birkhäuser. This book was released on 2012-12-06 with total page 373 pages. Available in PDF, EPUB and Kindle. Book excerpt: The year 2000 is the centenary year of the publication of Bachelier's thesis which - together with Harry Markovitz Ph. D. dissertation on portfolio selection in 1952 and Fischer Black's and Myron Scholes' solution of an option pricing problem in 1973 - is considered as the starting point of modern finance as a mathematical discipline. On this remarkable anniversary the workshop on mathematical finance held at the University of Konstanz brought together practitioners, economists and mathematicians to discuss the state of the art. Apart from contributions to the known discrete, Brownian, and Lvy process models, first attempts to describe a market in a reasonable way by a fractional Brownian motion model are presented, opening many new aspects for practitioners and new problems for mathematicians. As most dynamical financial problems are stochastic filtering or control problems many talks presented adaptations of control methods and techniques to the classical financial problems in portfolio selection irreversible investment risk sensitive asset allocation capital asset pricing hedging contingent claims option pricing interest rate theory. The contributions of practitioners link the theoretical results to the steadily increasing flow of real world problems from financial institutions into mathematical laboratories. The present volume reflects this exchange of theoretical and applied results, methods and techniques that made the workshop a fruitful contribution to the interdisciplinary work in mathematical finance.
Download or read book Relative Optimization of Continuous Time and Continuous State Stochastic Systems written by Xi-Ren Cao and published by Springer Nature. This book was released on 2020-05-13 with total page 376 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph applies the relative optimization approach to time nonhomogeneous continuous-time and continuous-state dynamic systems. The approach is intuitively clear and does not require deep knowledge of the mathematics of partial differential equations. The topics covered have the following distinguishing features: long-run average with no under-selectivity, non-smooth value functions with no viscosity solutions, diffusion processes with degenerate points, multi-class optimization with state classification, and optimization with no dynamic programming. The book begins with an introduction to relative optimization, including a comparison with the traditional approach of dynamic programming. The text then studies the Markov process, focusing on infinite-horizon optimization problems, and moves on to discuss optimal control of diffusion processes with semi-smooth value functions and degenerate points, and optimization of multi-dimensional diffusion processes. The book concludes with a brief overview of performance derivative-based optimization. Among the more important novel considerations presented are: the extension of the Hamilton–Jacobi–Bellman optimality condition from smooth to semi-smooth value functions by derivation of explicit optimality conditions at semi-smooth points and application of this result to degenerate and reflected processes; proof of semi-smoothness of the value function at degenerate points; attention to the under-selectivity issue for the long-run average and bias optimality; discussion of state classification for time nonhomogeneous continuous processes and multi-class optimization; and development of the multi-dimensional Tanaka formula for semi-smooth functions and application of this formula to stochastic control of multi-dimensional systems with degenerate points. The book will be of interest to researchers and students in the field of stochastic control and performance optimization alike.
