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SEMILAGRANGIAN SCHEMES FOR LINEAR AND FULLY NONLINEAR HAMILTONJACOBIBELLMAN EQUATIONS
"... (Communicated by the associate editor name) Abstract. We consider the numerical solution of HamiltonJacobiBellman equations arising in stochastic control theory. We introduce a class of monotone approximation schemes relying on monotone interpolation. These schemes converge under very weak assump ..."
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Cited by 10 (1 self)
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(Communicated by the associate editor name) Abstract. We consider the numerical solution of HamiltonJacobiBellman equations arising in stochastic control theory. We introduce a class of monotone approximation schemes relying on monotone interpolation. These schemes converge under very weak
A HamiltonJacobiBellman approach to optimal trade execution
, 2009
"... The optimal trade execution problem is formulated in terms of a meanvariance tradeoff, as seen at the initial time. The meanvariance problem can be embedded in a LinearQuadratic (LQ) optimal stochastic control problem, A semiLagrangian scheme is used to solve the resulting nonlinear Hamilton Ja ..."
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Cited by 16 (3 self)
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The optimal trade execution problem is formulated in terms of a meanvariance tradeoff, as seen at the initial time. The meanvariance problem can be embedded in a LinearQuadratic (LQ) optimal stochastic control problem, A semiLagrangian scheme is used to solve the resulting nonlinear Hamilton
Numerical solution of the HamiltonJacobiBellman formulation for continuous time mean variance asset allocation
 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 LinearQuadratic (LQ) problems using the method in (Zhou and Li, 2000; Li and Ng, 2000). We use a finite difference metho ..."
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Cited by 14 (4 self)
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method with fully implicit timestepping to solve the resulting nonlinear HamiltonJacobiBellman (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
, 2005
"... This paper considers linearquadratic control of a nonlinear dynamical system subject to arbitrary cost. I show that for this class of stochastic control problems the nonlinear HamiltonJacobiBellman equation can be transformed into a linear equation. The transformation is similar to the transfor ..."
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Cited by 59 (3 self)
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This paper considers linearquadratic control of a nonlinear dynamical system subject to arbitrary cost. I show that for this class of stochastic control problems the nonlinear HamiltonJacobiBellman equation can be transformed into a linear equation. The transformation is similar
Linear hamilton jacobi bellman equations in high dimensions
 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 ..."
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Cited by 7 (3 self)
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scales linearly with the number of states in a system, and is applicable to systems that are nonlinear with stochastic forcing in finitehorizon, average cost, and firstexit 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
"... 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 HamiltonJacobiBellman
, 2006
"... equations with respect to timespace shifts in a stationary ergodic medium ..."
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equations with respect to timespace shifts in a stationary ergodic medium
Approximate Solutions to the TimeInvariant HamiltonJacobiBellman Equation
, 1998
"... In this paper we develop a new method to approximate the solution to the HamiltonJacobiBellman (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 ..."
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Cited by 29 (4 self)
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In this paper we develop a new method to approximate the solution to the HamiltonJacobiBellman (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 SEMILAGRANGIAN SCHEME FOR FIRST ORDER HAMILTONJACOBI BELLMAN EQUATIONS
, 2012
"... We propose a semiLagrangian scheme using a spatially adaptive sparse grid to deal with nonlinear timedependent HamiltonJacobi 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 ..."
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Cited by 43 (5 self)
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We propose a semiLagrangian scheme using a spatially adaptive sparse grid to deal with nonlinear timedependent HamiltonJacobi 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 HamiltonJacobiBellman equations
, 2007
"... We obtain nonsymmetric upper and lower bounds on the rate of convergence of general monotone approximation/numerical schemes for parabolic HamiltonJacobiBellman equations by introducing a new notion of consistency. Our results are robust and general – they improve and extend earlier results by Kry ..."
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Cited by 84 (9 self)
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We obtain nonsymmetric upper and lower bounds on the rate of convergence of general monotone approximation/numerical schemes for parabolic HamiltonJacobiBellman equations by introducing a new notion of consistency. Our results are robust and general – they improve and extend earlier results
Results 1  10
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633