Abstract. In this paper, we describe our development of a higher-order method for solving the Hamilton-Jacobi-Bellman PDE by incorporating several techniques. There are the power series method of Albrecht, Cauchy-Kovalevskaya techniques, patchy methods of Ancona and Bressan and Navasca and Krener

PDEs where the Hamiltonian is given as (or well-approximated 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

of the dual-space semigroup corresponding to the HJB PDE. This dual-space semigroup is constructed from the dual-space semigroups corresponding to the constituent Hamiltonians. Copyright 2005 IFAC.

-space semigroup corresponding to the HJB PDE. This dual-space semigroup is constructed from the dual-space semigroups corresponding to the constituent linear/quadratic Hamiltonians. The dual-space semigroup is particularly useful due to its form as a max-plus integral operator with kernel obtained from

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

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

We propose the use of a mean–quadratic-variation 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

This paper deals with a numerical approximation of optimal controls by solving a Hamilton-Jacobi-Bellman (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

We consider the following economic problem: modelling the vintage capital structure of an economic system. The problem is naturally for-mulated as an optimal control problem where the state equation is either a first order PDE or a delay equation. The optimal state-control couple describe

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