scholarly journals A fully backward representation of semilinear PDEs applied to the control of thermostatic loads in power systems

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Lucas Izydorczyk ◽  
Nadia Oudjane ◽  
Francesco Russo
Keyword(s):  
Monte Carlo ◽  
Power Systems ◽  
Control Problem ◽  
Stochastic Control ◽  
Computational Efficiency ◽  
Value Function ◽  
Semilinear Pdes ◽  
Areas Of Interest ◽  
The Value Function

Abstract We propose a fully backward representation of semilinear PDEs with application to stochastic control. Based on this, we develop a fully backward Monte-Carlo scheme allowing to generate the regression grid, backwardly in time, as the value function is computed. This offers two key advantages in terms of computational efficiency and memory. First, the grid is generated adaptively in the areas of interest, and second, there is no need to store the entire grid. The performances of this technique are compared in simulations to the traditional Monte-Carlo forward-backward approach on a control problem of thermostatic loads.

A quasilinear elliptic equation in ℝN

1996 ◽  
Vol 126 (5) ◽  
pp. 911-921 ◽  
Author(s):  
O. Alvarez
Keyword(s):  
Lower Bound ◽  
Elliptic Equation ◽  
Control Problem ◽  
Stochastic Control ◽  
Quasilinear Elliptic Equation ◽  
Value Function ◽  
Optimal Criterion ◽  
Hamilton Jacobi Bellman ◽  
Quasilinear Elliptic ◽  
The Value Function

A quasilinear elliptic equation in ℝN of Hamilton-Jacobi-Bellman type is studied. An optimal criterion for uniqueness which involves only a lower bound on the functions is given. The unique solution in this class is identified as the value function of the associated stochastic control problem.

scholarly journals Optimal dividend and reinsurance in the presence of two reinsurers

2016 ◽  
Vol 53 (2) ◽  
pp. 554-571 ◽  
Author(s):  
Mi Chen ◽  
Kam Chuen Yuen
Keyword(s):  
Control Problem ◽  
Transaction Costs ◽  
Stochastic Control ◽  
Value Function ◽  
Optimal Reinsurance ◽  
Stochastic Control Problem ◽  
Optimal Dividend ◽  
The Impact ◽  
The Value Function ◽  
Limit Diffusion

Abstract In this paper the optimal dividend (subject to transaction costs) and reinsurance (with two reinsurers) problem is studied in the limit diffusion setting. It is assumed that transaction costs and taxes are required when dividends occur, and that the premiums charged by two reinsurers are calculated according to the exponential premium principle with different parameters, which makes the stochastic control problem nonlinear. The objective of the insurer is to determine the optimal reinsurance and dividend policy so as to maximize the expected discounted dividends until ruin. The problem is formulated as a mixed classical-impulse stochastic control problem. Explicit expressions for the value function and the corresponding optimal strategy are obtained. Finally, a numerical example is presented to illustrate the impact of the parameters associated with the two reinsurers' premium principle on the optimal reinsurance strategy.

scholarly journals Averaging of the Hamilton-Jacobi equation in infinite dimensions and an application

2000 ◽  
Vol 41 (3) ◽  
pp. 372-385
Author(s):  
Shihong Wang ◽  
Zuoyi Zhou
Keyword(s):  
Optimal Control ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Viscosity Solution ◽  
Jacobi Equation ◽  
Value Function ◽  
Limit Problem ◽  
Infinite Dimensions ◽  
The Value Function ◽  
Hamilton Jacobi Equation

AbstractWe study the averaging of the Hamilton-Jacobi equation with fast variables in the viscosity solution sense in infinite dimensions. We prove that the viscosity solution of the original equation converges to the viscosity solution of the averaged equation and apply this result to the limit problem of the value function for an optimal control problem with fast variables.

scholarly journals Stochastic optimal control problem with infinite horizon driven by G-Brownian motion

2018 ◽  
Vol 24 (2) ◽  
pp. 873-899 ◽  
Author(s):  
Mingshang Hu ◽  
Falei Wang
Keyword(s):  
Optimal Control ◽  
Brownian Motion ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Stochastic Optimal Control ◽  
Value Function ◽  
Infinite Horizon ◽  
Dynamic Programming Principle ◽  
Stochastic Optimal Control Problem ◽  
The Value Function

The present paper considers a stochastic optimal control problem, in which the cost function is defined through a backward stochastic differential equation with infinite horizon driven by G-Brownian motion. Then we study the regularities of the value function and establish the dynamic programming principle. Moreover, we prove that the value function is the unique viscosity solution of the related Hamilton−Jacobi−Bellman−Isaacs (HJBI) equation.

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