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摘要翻译：
我们研究了电力市场中的需求响应契约问题，通过量化考虑一个平均场的消费者的影响，该消费者的消费受到一个共同噪声的影响。我们将该问题描述为一个带有道德风险的委托代理问题，其中委托人她是一个电力生产者，她不断观察一个连续的风险厌恶消费者的消费，并设计合同以降低她的生产成本。更确切地说，生产者激励消费者降低其在不同用途中消费的平均数和波动性，而不注意他们所做的努力。我们证明了生产者可以从考虑消费者的平均场中受益，方法是将契约指数化到一个代理人的消费上，并将总消费统计量指数化到整个消费者人口的分布上。在线性能量估值的情况下，我们给出了这种新型最优合同的闭式表达式，使生产者的效用最大化。在大多数情况下，我们表明这种新型合同允许委托人选择她想要承担的风险，并将手头的问题减少到一个不相关的问题。
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英文标题：
《Mean-field moral hazard for optimal energy demand response management》
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作者：
Romuald Elie, Emma Hubert, Thibaut Mastrolia, Dylan Possama\"i
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最新提交年份：
2020
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分类信息：
一级分类：Mathematics 数学
二级分类：Probability 概率
分类描述：Theory and applications of probability and stochastic processes: e.g. central limit theorems, large deviations, stochastic differential equations, models from statistical mechanics, queuing theory
概率论与随机过程的理论与应用：例如中心极限定理，大偏差，随机微分方程，统计力学模型，排队论
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一级分类：Economics 经济学
二级分类：General Economics 一般经济学
分类描述：General methodological, applied, and empirical contributions to economics.
对经济学的一般方法、应用和经验贡献。
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一级分类：Mathematics 数学
二级分类：Optimization and Control 优化与控制
分类描述：Operations research, linear programming, control theory, systems theory, optimal control, game theory
运筹学，线性规划，控制论，系统论，最优控制，博弈论
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一级分类：Quantitative Finance 数量金融学
二级分类：Economics 经济学
分类描述：q-fin.EC is an alias for econ.GN. Economics, including micro and macro economics, international economics, theory of the firm, labor economics, and other economic topics outside finance
q-fin.ec是econ.gn的别名。经济学，包括微观和宏观经济学、国际经济学、企业理论、劳动经济学和其他金融以外的经济专题
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英文摘要：
We study the problem of demand response contracts in electricity markets by quantifying the impact of considering a mean-field of consumers, whose consumption is impacted by a common noise. We formulate the problem as a Principal-Agent problem with moral hazard in which the Principal - she - is an electricity producer who observes continuously the consumption of a continuum of risk-averse consumers, and designs contracts in order to reduce her production costs. More precisely, the producer incentivises the consumers to reduce the average and the volatility of their consumption in different usages, without observing the efforts they make. We prove that the producer can benefit from considering the mean-field of consumers by indexing contracts on the consumption of one Agent and aggregate consumption statistics from the distribution of the entire population of consumers. In the case of linear energy valuation, we provide closed-form expression for this new type of optimal contracts that maximises the utility of the producer. In most cases, we show that this new type of contracts allows the Principal to choose the risks she wants to bear, and to reduce the problem at hand to an uncorrelated one.
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PDF链接：
https://arxiv.org/pdf/1902.10405
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