scholarly journals Optimal Coordination Strategy for International Production Planning and Pollution Abating under Cap-and-Trade Regulations

2019 ◽  
Vol 16 (18) ◽  
pp. 3490 ◽  
Author(s):  
Baogui Xin ◽  
Wei Peng ◽  
Minghe Sun
Keyword(s):  
Production Planning ◽  
Cap And Trade ◽  
Hjb Equations ◽  
Coordination Strategies ◽  
Coordination Strategy ◽  
International Production ◽  
Optimal Coordination ◽  
Hamilton Jacobi Bellman ◽  
Pollution Emissions ◽  
Cooperative Differential Games

Because both pollution emissions and production policies often are international in scope, it is necessary to find optimal coordination strategies for international production planning and pollution abating. Differential game models are developed for multiple neighboring countries to reach optimal decisions on their production planning and pollution abating under cap-and-trade regulations. Non-cooperative and cooperative differential games are presented to depict the optimal tradeoffs between production planning and pollution abating. Hamilton-Jacobi-Bellman (HJB) equations are then employed to analyze the asymmetric and symmetric feedback solutions. Numerical simulations are used to illustrate the results. Five different dividends are also discussed. With the proposed strategies, more improvement will be directed toward production supplies and environmental issues than ever before.

scholarly journals Policy iteration for Hamilton–Jacobi–Bellman equations with control constraints

2021 ◽  
Author(s):  
Sudeep Kundu ◽  
Karl Kunisch
Keyword(s):  
Linear Equations ◽  
Hjb Equation ◽  
Policy Iteration ◽  
Optimal Feedback Control ◽  
Iteration Step ◽  
Control Constraints ◽  
Hjb Equations ◽  
Bellman Equations ◽  
Hamilton Jacobi Bellman ◽  
Feedback Control Theory

AbstractPolicy iteration is a widely used technique to solve the Hamilton Jacobi Bellman (HJB) equation, which arises from nonlinear optimal feedback control theory. Its convergence analysis has attracted much attention in the unconstrained case. Here we analyze the case with control constraints both for the HJB equations which arise in deterministic and in stochastic control cases. The linear equations in each iteration step are solved by an implicit upwind scheme. Numerical examples are conducted to solve the HJB equation with control constraints and comparisons are shown with the unconstrained cases.

Do Time Preferences Matter in Intertemporal Consumption and Portfolio Decisions?

2019 ◽  
Vol 19 (2) ◽  
Author(s):  
Shou Chen ◽  
Shengpeng Xiang ◽  
Hongbo He
Keyword(s):  
Absolute Risk ◽  
Hyperbolic Discounting ◽  
Time Preferences ◽  
Hjb Equations ◽  
Portfolio Decisions ◽  
Special Cases ◽  
Intertemporal Consumption ◽  
Hamilton Jacobi Bellman ◽  
Hara Utility ◽  
Exponential Discounting

Abstract We study the intertemporal consumption and portfolio rules in the model with the general hyperbolic absolute risk aversion (HARA) utility. The equivalent approximation approach is employed to obtain the Hamilton-Jacobi-Bellman (HJB) equations, and a remarkable property is shown: portfolio rules are independent of the discount function. Moreover, both the consumption and portfolio rates are non-increasing functions of wealth. Particularly illustrative cases examined in detail are the models with the most adopted discount functions, including exponential discounting and hyperbolic discounting. Explicit solutions for intertemporal decisions are found for these special cases, revealing that individual’s time preferences affect the consumption rules only. Moreover, the time-consistent consumption rate under hyperbolic discounting is larger than its counterpart under exponential discounting.

NATURAL GAS-FIRED POWER PLANTS VALUATION AND OPTIMIZATION UNDER LÉVY COPULAS AND REGIME SWITCHING

2017 ◽  
Vol 20 (01) ◽  
pp. 1750004 ◽  
Author(s):  
NEMAT SAFAROV ◽  
COLIN ATKINSON
Keyword(s):  
Natural Gas ◽  
Regime Switching ◽  
Power Plants ◽  
Control Strategies ◽  
Numerical Approach ◽  
Spot Price ◽  
Operating Characteristics ◽  
Hjb Equations ◽  
Explicit Finite Difference ◽  
Hamilton Jacobi Bellman

In this work, we analyze a stochastic control problem for the valuation of a natural gas power station while taking into account operating characteristics. Both electricity and gas spot price processes exhibit mean-reverting spikes and Markov regime-switches. The Lévy regime-switching model incorporates the effects of demand-supply fluctuations in energy markets and abrupt economic disruptions or business cycles. We make use of skewed Lévy copulas to model the dependence risk of electricity and gas jumps. The corresponding coupled Hamilton–Jacobi–Bellman (HJB) equations are solved by an explicit finite difference method. The numerical approach gives us both the value of the plant and its optimal operating strategy depending on the gas and electricity prices, current temperature of the boiler and time. The surfaces of control strategies and contract values are obtained by implementing the numerical method for a particular example.

scholarly journals How People Initiate Energy Optimization and Converge on Their Optimal Gaits

2018 ◽  
Author(s):  
Jessica Selinger ◽  
Jeremy Wong ◽  
Surabhi Simha ◽  
Maxwell Donelan
Keyword(s):  
Nervous System ◽  
Reinforcement Learning ◽  
Energy Optimization ◽  
Coordination Strategies ◽  
Human Experiments ◽  
Optimal Coordination ◽  
Optimal Gait ◽  
Reinforcement Learning Models ◽  
The Cost ◽  
The Relationship

A central principle in motor control is that the coordination strategies learned by our nervous system are often optimal. Here we combined human experiments with computational reinforcement learning models to study how the nervous system navigates possible movements to arrive at an optimal coordination. Our experiments used robotic exoskeletons to reshape the relationship between how participants walk and how much energy they consume. We found that while some participants used their relatively high natural gait variability to explore the new energetic landscape and spontaneously initiate energy optimization, most participants preferred to exploit their originally preferred, but now suboptimal, gait. We could nevertheless reliably initiate optimization in these exploiters by providing them with the experience of lower cost gaits suggesting that the nervous system benefits from cues about the relevant dimensions along which to re-optimize its coordination. Once optimization was initiated, we found that the nervous system employed a local search process to converge on the new optimum gait over tens of seconds. Once optimization was completed, the nervous system learned to predict this new optimal gait and rapidly returned to it within a few steps if perturbed away. We model this optimization process as reinforcement learning and find behavior that closely matches these experimental observations. We conclude that the nervous system optimizes for energy using a prediction of the optimal gait, and then refines this prediction with the cost of each new walking step.

scholarly journals Optimal Coordination Strategies for Load Service Entity and Community Energy Systems Based on Centralized and Decentralized Approaches

Energies ◽  
2020 ◽  
Vol 13 (12) ◽  
pp. 3202
Author(s):  
Longxi Li
Keyword(s):  
Energy Demand ◽  
Numerical Study ◽  
Storage System ◽  
Energy Systems ◽  
Energy Prices ◽  
Renewable Energy Resources ◽  
Coordination Strategies ◽  
Coordination Scheme ◽  
Game Theoretic ◽  
Optimal Coordination

The energy interaction among a load service entity and community energy systems in neighboring communities leads to a complex energy generation, storage, and transaction problem. A load service entity is formed by a local electricity generation system, storage system, and renewable energy resources, which can provide ancillary services to customers and the utility grid. This paper proposes two coordination schemes for the interaction of community-based energy systems and load service entities based on game-theoretic frameworks. The first one is a centralized coordination scheme with full cooperation, in which the load service entity and community energy systems jointly activate the local resources. The second one is set as a decentralized coordination scheme to obtain a relative balance of interests among the market participants in a Stackelberg framework. Two mathematical models are developed for the day-ahead decision-making of the above energy management schemes. The Shapley value method, Karush-Kuhn-Tucker conditions, and strong dual theory are applied to solve the complex coordination problems. Numerical study shows the effectiveness of the coordination strategies that all stakeholders benefit from the proposed coordination schemes and create a win–win situation. In addition, sensitivity analysis is conducted to study the effects of system configuration, energy demand, and energy prices on the economic performance of all stakeholders. The results can serve as references for business managers of the load service entity.

Optimal Insurance-Package and Investment Problem for an Insurer

2018 ◽  
Vol 6 (1) ◽  
pp. 85-96
Author(s):  
Delei Sheng ◽  
Linfang Xing
Keyword(s):  
Value Function ◽  
Investment Strategy ◽  
Optimal Combination ◽  
Hjb Equations ◽  
Terminal Wealth ◽  
Optimal Insurance ◽  
Yield Rate ◽  
Investment Problem ◽  
Hamilton Jacobi Bellman ◽  
The Value Function

AbstractAn insurance-package is a combination being tie-in at least two different categories of insurances with different underwriting-yield-rate. In this paper, the optimal insurance-package and investment problem is investigated by maximizing the insurer’s exponential utility of terminal wealth to find the optimal combination-share and investment strategy. Using the methods of stochastic analysis and stochastic optimal control, the Hamilton-Jacobi-Bellman (HJB) equations are established, the optimal strategy and the value function are obtained in closed form. By comparing with classical results, it shows that the insurance-package can enhance the utility of terminal wealth, meanwhile, reduce the insurer’s claim risk.

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