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Risk Averse Optimal Control Of Diffusion Processes
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Book Synopsis Risk-averse Optimal Control of Diffusion Processes by : Jianing Yao
Download or read book Risk-averse Optimal Control of Diffusion Processes written by Jianing Yao and published by . This book was released on 2017 with total page 86 pages. Available in PDF, EPUB and Kindle. Book excerpt: This work analyzes an optimal control problem for which the performance is measured by a dynamic risk measure. While dynamic risk measures in discrete-time and the control problems associated are well understood, the continuous-time framework brings great challenges both in theory and practice. This study addresses modeling, numerical schemes and applications. In the first part, we focus on the formulation of a risk-averse control problem. Specifically, we make use of a decoupled forward-backward system of stochastic differential equations to evaluate a fixed policy: the forward stochastic differential equation (SDE) characterizes the evolution of states, and the backward stochastic differential equation (BSDE) does the risk evaluation at any instant of time. Relying on the Markovian structure of the system, we obtain the corresponding dynamic programming equation via weak formulation and strong formulation; in the meanwhile, the risk-averse Hamilton-Jacobi-Bellman equation and its verification are derived under suitable assumptions. In the second part, the main thrust is to find a convergent numerical method to solve the system in discrete-time setting. Specifically, we construct a piecewise-constant Markovian control to show its arbitrarily closeness to the optimal control. The results heavily relies on the regularity of the solution to generalized Hamilton-Jacobi-Bellman PDE. In the third part, we propose a numerical method for risk evaluation defined by BSDE. Using dual representation of the risk measure, we converted risk valuation to a stochastic control problem, where the control is the Radon-Nikodym derivative process. The optimality conditions of such control problem enables us to use a piecewise-constant density (control) to arrive at a close approximation on a short interval. Then, the Bellman principle extends the approximation to any finite time horizon problem. Lastly, we give a financial application in risk management in conjunction with nested simulation.
Book Synopsis Optimal Control of Diffusion Processes by : Vivek S. Borkar
Download or read book Optimal Control of Diffusion Processes written by Vivek S. Borkar and published by Longman. This book was released on 1989 with total page 212 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis On the Optimal Control of Diffusion Processes by : Martin Lee Puterman
Download or read book On the Optimal Control of Diffusion Processes written by Martin Lee Puterman and published by . This book was released on 1972 with total page 100 pages. Available in PDF, EPUB and Kindle. Book excerpt: The author considers three problems in the optimal control of diffusion processes. The first is that of optimally controlling a diffusion process on a compact interval. The second problem is that of optimally controlling a diffusion process on a bounded subset of Euclidean n-space, with refledtion on the boundary. The last problem arises in controlling a continuous time production process. (Author).
Book Synopsis Optimal Control of Diffusion Processes by : Wendell H. Fleming
Download or read book Optimal Control of Diffusion Processes written by Wendell H. Fleming and published by . This book was released on 1972 with total page 14 pages. Available in PDF, EPUB and Kindle. Book excerpt: The paper summarizes some recent work on optimal control theory for continuous parameter stochastic processes. The author discusses only the control of Markov diffusion processes governed by stochastic differential equations of Ito type. Moreover, the author considers only the two cases when either: (A) no observations are available to the controller (open loop control); or (B) the states of the processes are completely observed by the controller. (Author).
Book Synopsis Optimal Control of Diffusion Processes and Hamilton-Jacobi-Bellman Equations by : Pierre-Louis Lions
Download or read book Optimal Control of Diffusion Processes and Hamilton-Jacobi-Bellman Equations written by Pierre-Louis Lions and published by . This book was released on 1983 with total page 74 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Optimal Control of a Class of Diffusion Processes by : Jerome Barry Shapiro
Download or read book Optimal Control of a Class of Diffusion Processes written by Jerome Barry Shapiro and published by . This book was released on 1970 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Optimal Control of Diffusion Processes with Discontinuous Coefficients by : Keigo Yamada
Download or read book Optimal Control of Diffusion Processes with Discontinuous Coefficients written by Keigo Yamada and published by . This book was released on 1972 with total page 122 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Controlled Diffusion Processes by : Nikolaĭ Vladimirovich Krylov
Download or read book Controlled Diffusion Processes written by Nikolaĭ Vladimirovich Krylov and published by . This book was released on 1980 with total page 328 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Linear-Quadratic Controls in Risk-Averse Decision Making by : Khanh D. Pham
Download or read book Linear-Quadratic Controls in Risk-Averse Decision Making written by Khanh D. Pham and published by Springer Science & Business Media. This book was released on 2012-10-23 with total page 157 pages. Available in PDF, EPUB and Kindle. Book excerpt: Linear-Quadratic Controls in Risk-Averse Decision Making cuts across control engineering (control feedback and decision optimization) and statistics (post-design performance analysis) with a common theme: reliability increase seen from the responsive angle of incorporating and engineering multi-level performance robustness beyond the long-run average performance into control feedback design and decision making and complex dynamic systems from the start. This monograph provides a complete description of statistical optimal control (also known as cost-cumulant control) theory. In control problems and topics, emphasis is primarily placed on major developments attained and explicit connections between mathematical statistics of performance appraisals and decision and control optimization. Chapter summaries shed light on the relevance of developed results, which makes this monograph suitable for graduate-level lectures in applied mathematics and electrical engineering with systems-theoretic concentration, elective study or a reference for interested readers, researchers, and graduate students who are interested in theoretical constructs and design principles for stochastic controlled systems.
Book Synopsis Optimal Control of Diffusion Processes and Hamilton-Jacobi-Bellman Equations by : Pierre-Louis Lions
Download or read book Optimal Control of Diffusion Processes and Hamilton-Jacobi-Bellman Equations written by Pierre-Louis Lions and published by . This book was released on 1983 with total page 48 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Modeling and Optimization: Theory and Applications by : Martin Takáč
Download or read book Modeling and Optimization: Theory and Applications written by Martin Takáč and published by Springer. This book was released on 2017-10-30 with total page 164 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains a selection of contributions that were presented at the Modeling and Optimization: Theory and Applications Conference (MOPTA) held at Lehigh University in Bethlehem, Pennsylvania, USA on August 17-19, 2016. The conference brought together a diverse group of researchers and practitioners, working on both theoretical and practical aspects of continuous or discrete optimization. Topics presented included algorithms for solving convex, network, mixed-integer, nonlinear, and global optimization problems, and addressed the application of deterministic and stochastic optimization techniques in energy, finance, logistics, analytics, health, and other important fields. The contributions contained in this volume represent a sample of these topics and applications and illustrate the broad diversity of ideas discussed at the meeting.
Book Synopsis Optimal Control of Counterflow Diffusion Processes by : E. M. Stafford
Download or read book Optimal Control of Counterflow Diffusion Processes written by E. M. Stafford and published by . This book was released on 1969 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Optimal Control Problems in diffusion processes with a nonsmooth nonlinear boundary condition by : Eckehard Sachs
Download or read book Optimal Control Problems in diffusion processes with a nonsmooth nonlinear boundary condition written by Eckehard Sachs and published by . This book was released on 1981 with total page 27 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Optimal Control and Nonlinear Filtering for Nondegenerate Diffusion Processes by : Wendell Helms Fleming
Download or read book Optimal Control and Nonlinear Filtering for Nondegenerate Diffusion Processes written by Wendell Helms Fleming and published by . This book was released on 1981 with total page 40 pages. Available in PDF, EPUB and Kindle. Book excerpt: A linear parabolic partial differential equation describing the pathwise filter for a nondegenerate diffusion is changed, by an expotential substitution, into the dynamic programming equation of an optimal stochastic control problem. This substitution is applied to obtain results about the rate of decay as the numerical value of chi approaches infinity of solutions p(chi, tau) to the pathwise filter equation, and for solutions of the corresponding Zakai equation.
Book Synopsis Risk-Sensitive Optimal Control by : Peter Whittle
Download or read book Risk-Sensitive Optimal Control written by Peter Whittle and published by . This book was released on 1990-05-11 with total page 266 pages. Available in PDF, EPUB and Kindle. Book excerpt: The two major themes of this book are risk-sensitive control and path-integral or Hamiltonian formulation. It covers risk-sensitive certainty-equivalence principles, the consequent extension of the conventional LQG treatment and the path-integral formulation.
Book Synopsis Ergodic Control of Diffusion Processes by : Ari Arapostathis
Download or read book Ergodic Control of Diffusion Processes written by Ari Arapostathis and published by Cambridge University Press. This book was released on 2012 with total page 341 pages. Available in PDF, EPUB and Kindle. Book excerpt: The first comprehensive account of controlled diffusions with a focus on ergodic or 'long run average' control.
Book Synopsis Some Problems in the Optimal Control of Diffusions by : Diane Sheng
Download or read book Some Problems in the Optimal Control of Diffusions written by Diane Sheng and published by . This book was released on 1978 with total page 134 pages. Available in PDF, EPUB and Kindle. Book excerpt: We consider a class of problems in the optimal control of one-dimensional diffusion processes, with the objective to minimize expected discounted cost over an infinite planning horizon. There are available a finite number of control modes (actions), and the state of the system changes locally like a Brownian Motion whose drift and variance depend upon the control mode being employed (but not upon the current state). There is a holding cost which is proportional to the state of the system and is independent of the control mode. In addition to these continuous costs, there are lump costs associated with a change in action. The state space may be either a finite or semi-infinite interval, and different types of boundary behavior are considered. Absorbing barriers arise in applications to collective risk and insurance, while reflecting barriers are natural for problems in the optimal control of queueing and storage systems. When there are only two control modes, one expects an optimal policy characterized by a pair of critical numbers. For various special cases, it is shown that such an optimal policy exists, and (complicated) formulas for the critical numbers are derived. (Author).
