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The Patchy Cost and Feedback for the HJB PDE
"... Abstract. In this paper, we describe our development of a higherorder method for solving the HamiltonJacobiBellman PDE by incorporating several techniques. There are the power series method of Albrecht, CauchyKovalevskaya techniques, patchy methods of Ancona and Bressan and Navasca and Krener, t ..."
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Abstract. In this paper, we describe our development of a higherorder method for solving the HamiltonJacobiBellman PDE by incorporating several techniques. There are the power series method of Albrecht, CauchyKovalevskaya techniques, patchy methods of Ancona and Bressan and Navasca and Krener
CurseofComplexity Attenuation in the CurseofDimensionalityFree Method for HJB PDEs,
 Proc. ACC
, 2008
"... AbstractRecently, a curseofdimensionalityfree method was developed for solution of HamiltonJacobiBellman partial differential equations (HJB PDEs) for nonlinear control problems, using semiconvex duality and maxplus analysis. The curseofdimensionalityfree method may be applied to HJB PDEs ..."
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Cited by 15 (7 self)
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PDEs where the Hamiltonian is given as (or wellapproximated by) a pointwise maximum of quadratic forms. Such HJB PDEs also arise in certain switched linear systems. The method constructs the correct solution of an HJB PDE from a maxplus linear combination of quadratics. The method completely avoids
A CurseofDimensionalityFree Numerical Method for a Class of HJB PDEs
 Proc. 16th IFAC World Congress
, 2005
"... Abstract: Maxplus methods have been explored for solution of firstorder, nonlinear HamiltonJacobiBellman partial differential equations (HJB PDEs) and corresponding nonlinear control problems. These methods exploit the maxplus linearity of the associated semigroups. Although these methods pro ..."
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Cited by 17 (7 self)
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of the dualspace semigroup corresponding to the HJB PDE. This dualspace semigroup is constructed from the dualspace semigroups corresponding to the constituent Hamiltonians. Copyright 2005 IFAC.
Convergence rate for a curseofdimensionalityfree method for a class of HJB PDEs
 SIAM J. Control Optim
"... Abstract. In previous work of the first author and others, maxplus methods have been explored for solution of firstorder, nonlinear HamiltonJacobiBellman partial differential equations (HJB PDEs) and corresponding nonlinear control problems. Although maxplus basis expansion and maxplus finite ..."
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Cited by 8 (3 self)
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space semigroup corresponding to the HJB PDE. This dualspace semigroup is constructed from the dualspace semigroups corresponding to the constituent linear/quadratic Hamiltonians. The dualspace semigroup is particularly useful due to its form as a maxplus integral operator with kernel obtained from
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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Jacobi Bellman (HJB) PDE. This method is essentially independent of the form for the price impact functions. Provided a strong comparision property holds, we prove that the numerical scheme converges to the viscosity solution of the HJB PDE. Numerical examples are presented in terms of the efficient
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
Optimal Trade Execution: A Mean–QuadraticVariation Approach
, 2009
"... We propose the use of a mean–quadraticvariation criteria to determine an optimal trading strategy in the presence of price impact. We derive the Hamilton Jacobi Bellman (HJB) Partial Differential Equation (PDE) for the optimal strategy, assuming the underlying asset follows Geometric Brownian Motio ..."
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Cited by 8 (0 self)
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We propose the use of a mean–quadraticvariation criteria to determine an optimal trading strategy in the presence of price impact. We derive the Hamilton Jacobi Bellman (HJB) Partial Differential Equation (PDE) for the optimal strategy, assuming the underlying asset follows Geometric Brownian
Approximation of optimal controls for semilinear parabolic PDE by solving HamiltonJacobiBellman equations
"... This paper deals with a numerical approximation of optimal controls by solving a HamiltonJacobiBellman (HJB) equation, corresponding to control problems of parabolic PDE. The method is based on a model reduction, using POD (Proper Orthogonal Decomposition), and on the approximation of the HJB equa ..."
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Cited by 1 (0 self)
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This paper deals with a numerical approximation of optimal controls by solving a HamiltonJacobiBellman (HJB) equation, corresponding to control problems of parabolic PDE. The method is based on a model reduction, using POD (Proper Orthogonal Decomposition), and on the approximation of the HJB
Dynamic programming methods for Optimal Con trol of PDE’s arising in Economics
"... We consider the following economic problem: modelling the vintage capital structure of an economic system. The problem is naturally formulated as an optimal control problem where the state equation is either a first order PDE or a delay equation. The optimal statecontrol couple describe the behavi ..."
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We consider the following economic problem: modelling the vintage capital structure of an economic system. The problem is naturally formulated as an optimal control problem where the state equation is either a first order PDE or a delay equation. The optimal statecontrol couple describe
Bertrand & Cournot Mean Field Games
, 2014
"... We study how continuous time Bertrand and Cournot competitions, in which firms producing similar goods compete with one another by setting prices or quantities respectively, can be analyzed as continuum dynamic mean field games. Interactions are of mean field type in the sense that the demand faced ..."
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Cited by 1 (1 self)
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is characterized by a coupled system of partial differential equations: a backward HJB PDE for the value function, and a forward Kolmogorov PDE for the density of players. Asymptotic approximation enables us to deduce certain qualitative features of the game in the limit of small competition. The equilibrium
Results 1  10
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24