the homogeneous balance method can be used to construct exact traveling wave solutions of nonlinear partial differential equations. in this paper, this method is used to construct newsoliton solutions of the (3+1) jimbo--miwa equation.

in this paper, the solution of the evolutionaryfourth-order in space, sivashinsky equation is obtained by meansof homotopy perturbation method (textbf{hpm}). the results revealthat the method is very effective, convenient  and quite accurateto systems of nonlinear partial differential equations.

We consider an optimal control problem of linear stochastic integro-differential equation with conic constraints on the phase variable and the control of singular-regular type. Our setting includes consumption-investment problems for models of financial markets in the presence of proportional transaction costs where that the prices are geometric Lévy processes and the investor is allowed to tak...

We develop a computationally efficient learning-based forward–backward stochastic differential equations (FBSDE) controller for both continuous and hybrid dynamical (HD) systems subject to noise state constraints. Solutions optimal control (SOC) problems satisfy the Hamilton–Jacobi–Bellman (HJB) equation. Using current FBSDE-based solutions, can be obtained from HJB using deep neural networks (...

Many problems in finance can be posed in terms of an optimal stochastic control. Some well-known examples include transaction cost/uncertain volatility models [17, 2, 25], passport options [1, 26], unequal borrowing/lending costs in option pricing [9], risk control in reinsurance [23], optimal withdrawals in variable annuities[13], optimal execution of trades [20, 19], and asset allocation [28,...

Classical geometric mechanics, including the study of symmetries, Lagrangian and Hamiltonian Hamilton-Jacobi theory, are founded on structures such as jets, symplectic contact ones. In this paper, we shall use a partly forgotten framework second-order (or stochastic) differential geometry, developed originally by L. Schwartz P.-A. Meyer, to construct counterparts those classical structures. The...

In this paper we investigate new approaches to dynamic-programming-based optimal control of continuous time-and-space systems. We use neural networks to approximate the solution to the Hamilton-Jacobi-Bellman (HJB) equation which is, in the deterministic case studied here, a rst-order, non-linear, partial diierential equation. We derive the gradient descent rule for integrating this equation in...

In this paper we investigate new approaches to dynamic-programming-based optimal control of continuous time-and-space systems. We use neural networks to approximate the solution to the Hamilton-Jacobi-Bellman (HJB) equation which is, in the deterministic case studied here, a rst-order, non-linear, partial di erential equation. We derive the gradient descent rule for integrating this equation in...

The valuation of a gas storage facility is characterized as a stochastic control problem, resulting in a Hamilton-Jacobi-Bellman (HJB) equation. In this paper, we present a semi-Lagrangian method for solving the HJB equation for a typical gas storage valuation problem. The method is able to handle a wide class of spot price models that exhibit mean-reverting, seasonality dynamics and price jump...