Results 1 - 10 of 633

SEMI-LAGRANGIAN SCHEMES FOR LINEAR AND FULLY NON-LINEAR HAMILTON-JACOBI-BELLMAN EQUATIONS

by Kristian Debrabant, Espen Robstad Jakobsen
"... (Communicated by the associate editor name) Abstract. We consider the numerical solution of Hamilton-Jacobi-Bellman equations arising in stochastic control theory. We introduce a class of mono-tone approximation schemes relying on monotone interpolation. These schemes converge under very weak assump ..."
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(Communicated by the associate editor name) Abstract. We consider the numerical solution of Hamilton-Jacobi-Bellman equations arising in stochastic control theory. We introduce a class of mono-tone approximation schemes relying on monotone interpolation. These schemes converge under very weak

A Hamilton-Jacobi-Bellman approach to optimal trade execution

by Peter A. Forsyth , 2009
"... The optimal trade execution problem is formulated in terms of a mean-variance tradeoff, as seen at the initial time. The mean-variance problem can be embedded in a Linear-Quadratic (LQ) optimal stochastic control problem, A semi-Lagrangian scheme is used to solve the resulting non-linear Hamilton Ja ..."
Abstract - Cited by 16 (3 self) - Add to MetaCart
The optimal trade execution problem is formulated in terms of a mean-variance tradeoff, as seen at the initial time. The mean-variance problem can be embedded in a Linear-Quadratic (LQ) optimal stochastic control problem, A semi-Lagrangian scheme is used to solve the resulting non-linear Hamilton

Numerical solution of the Hamilton-Jacobi-Bellman formulation for continuous time mean variance asset allocation

by J. Wang, P. A. Forsyth - IN THE JOURNAL OF ECONOMIC DYNAMICS AND CONTROL , 2009
"... We solve the optimal asset allocation problem using a mean variance approach. The original mean variance optimization problem can be embedded into a class of auxiliary stochastic Linear-Quadratic (LQ) problems using the method in (Zhou and Li, 2000; Li and Ng, 2000). We use a finite difference metho ..."
Abstract - Cited by 14 (4 self) - Add to MetaCart
method with fully implicit timestepping to solve the resulting non-linear Hamilton-Jacobi-Bellman (HJB) PDE, and present the solutions in terms of an efficient frontier and an optimal asset allocation strategy. The numerical scheme satisfies sufficient conditions to ensure convergence to the viscosity

Path integrals and symmetry breaking for optimal control theory

by H.J. Kappen , 2005
"... This paper considers linear-quadratic control of a non-linear dynamical system subject to arbitrary cost. I show that for this class of stochastic control problems the non-linear Hamilton-Jacobi-Bellman equation can be transformed into a linear equation. The transformation is similar to the transfor ..."
Abstract - Cited by 59 (3 self) - Add to MetaCart
This paper considers linear-quadratic control of a non-linear dynamical system subject to arbitrary cost. I show that for this class of stochastic control problems the non-linear Hamilton-Jacobi-Bellman equation can be transformed into a linear equation. The transformation is similar

Linear hamilton jacobi bellman equations in high dimensions

by Matanya B. Horowitz, Anil Damle, Joel W. Burdick - in Conference on Decision and Control (CDC), 2014, arXiv preprint arXiv:1404.1089
"... provides the globally optimal solution to large classes of control problems. Unfortunately, this generality comes at a price, the calculation of such solutions is typically intractible for systems with more than moderate state space size due to the curse of dimensionality. This work combines recent ..."
Abstract - Cited by 7 (3 self) - Add to MetaCart
scales linearly with the number of states in a system, and is applicable to systems that are nonlinear with stochastic forcing in finite-horizon, average cost, and first-exit settings. The method is demonstrated on inverted pendulum, VTOL aircraft, and quadcopter models, with system dimension two, six

Homogenization of random Hamilton–Jacobi–Bellman Equations

by S. R. Srinivasa Varadhan, Na D
"... ABSTRACT. We consider nonlinear parabolic equations of Hamilton–Jacobi– Bellman type. The Lagrangian is assumed to be convex, but with a spatial dependence which is stationary and random. Rescaling in space and time produces a similar equation with a rapidly varying spatial dependence and a small vi ..."
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ABSTRACT. We consider nonlinear parabolic equations of Hamilton–Jacobi– Bellman type. The Lagrangian is assumed to be convex, but with a spatial dependence which is stationary and random. Rescaling in space and time produces a similar equation with a rapidly varying spatial dependence and a small

Homogenization of Hamilton-Jacobi-Bellman

by Elena Kosygina, Srinivasa R. S. Varadhan , 2006
"... equations with respect to time-space shifts in a stationary ergodic medium ..."
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equations with respect to time-space shifts in a stationary ergodic medium

Approximate Solutions to the Time-Invariant Hamilton-Jacobi-Bellman Equation

by R. W. Beard, G. N. Saridis, J. T. Wen , 1998
"... In this paper we develop a new method to approximate the solution to the Hamilton-JacobiBellman (HJB) equation which arises in optimal control when the plant is modeled by nonlinear dynamics. The approximation is comprised of two steps. First, successive approximation is used to reduce the HJB equat ..."
Abstract - Cited by 29 (4 self) - Add to MetaCart
In this paper we develop a new method to approximate the solution to the Hamilton-JacobiBellman (HJB) equation which arises in optimal control when the plant is modeled by nonlinear dynamics. The approximation is comprised of two steps. First, successive approximation is used to reduce the HJB

AN ADAPTIVE SPARSE GRID SEMI-LAGRANGIAN SCHEME FOR FIRST ORDER HAMILTON-JACOBI BELLMAN EQUATIONS

by Olivier Bokanowski, Jochen Garcke, Michael Griebel, Irene Klompmaker , 2012
"... We propose a semi-Lagrangian scheme using a spatially adaptive sparse grid to deal with non-linear time-dependent Hamilton-Jacobi Bellman equations. We focus in particular on front propagation models in higher dimensions which are related to control problems. We test the numerical efficiency of the ..."
Abstract - Cited by 43 (5 self) - Add to MetaCart
We propose a semi-Lagrangian scheme using a spatially adaptive sparse grid to deal with non-linear time-dependent Hamilton-Jacobi Bellman equations. We focus in particular on front propagation models in higher dimensions which are related to control problems. We test the numerical efficiency

Error bounds for monotone approximation schemes for Hamilton-Jacobi-Bellman equations

by Guy Barles, Espen R. Jakobsen , 2007
"... We obtain nonsymmetric upper and lower bounds on the rate of convergence of general monotone approximation/numerical schemes for parabolic Hamilton-Jacobi-Bellman equations by introducing a new notion of consistency. Our results are robust and general – they improve and extend earlier results by Kry ..."
Abstract - Cited by 84 (9 self) - Add to MetaCart
We obtain nonsymmetric upper and lower bounds on the rate of convergence of general monotone approximation/numerical schemes for parabolic Hamilton-Jacobi-Bellman equations by introducing a new notion of consistency. Our results are robust and general – they improve and extend earlier results
Results 1 - 10 of 633