We characterize the value of swing contracts in continuous time as the unique viscosity solution of a Hamilton-Jacobi-Bellman equation with suitable boundary conditions. The case of contracts with penalties is straightforward, and in that case only a terminal condition is needed. Conversely, the case of contracts with strict constraints gives rise to a stochastic control problem with a nonstand...

This paper addresses the observer-based event-triggered optimal control (ETOC) for unknown nonlinear Ito^-type stochastic multi-agent systems (SMASs) with input constraints. To begin with, Hamilton-Jacobi-Bellman (HJB) equation constraints is presented, and a sufficient criterion on mean-square leader-following consensus of constrained-input SMASs derived. Next, novel policy iteration algorithm...

This work investigates the impact of taxation on an investment strategy insurance company considering three utility functions; exponential, power, and logarithmic preferences. The risky asset is assumed to be driven by Constant Elasticity Variance (CEV) model. problem considered was that trades two assets; a stock with behavior in presence stochastic cash flow or risk process money market accou...

In the past decade, there are many works on finite element methods for fully nonlinear Hamilton–Jacobi–Bellman (HJB) equations with Cordes condition. The linearised systems have large condition numbers, which depend not only mesh size but also parameters in This paper is concerned design and analysis of auxiliary space preconditioners a $$C^0$$ discretization HJB [Calcolo, 58, 2021]. Based stab...

E.I.Verriest and F.L.Lewis have presented in [1] a new method to approach the minimum-time control of linear continous-time systems avoiding the Bang-Bang control. Their method relied on the optimization of a cost including time energy and precisions terms. Then, N.Elalami and N.Znaidi [2], extended these results to the discrete-time linear systems. The objective of this work is to propose an a...

Abstract Stochastic optimal principle leads to the resolution of a partial differential equation (PDE), namely Hamilton–Jacobi–Bellman (HJB) equation. In general, this cannot be solved analytically, thus numerical algorithms are only tools provide accurate approximations. The aims paper is introduce novel fitted finite volume method solve high dimensional degenerated HJB from stochastic control...

We treat infinite horizon optimal control problems by solving the associated stationary Hamilton-Jacobi-Bellman (HJB) equation numerically to compute value function and an feedback law. The dynamical systems under consideration are spatial discretizations of non linear parabolic partial differential equations (PDE), which means that HJB is suffers from curse dimensionality. Its linearity handle...

A solution of a discrete Hamilton–Jacobi–Bellman equation is represented in terms of idempotent analysis as a convergent series of integral operators.

We consider an optimal investment and consumption problem for a Black-Scholes financial market with stochastic coefficients driven by a diffusion process. We assume that an agent makes consumption and investment decisions based on CRRA utility functions. The dynamical programming approach leads to an investigation of the Hamilton Jacobi Bellman (HJB) equation which is a highly non linear partia...