论文标题
能源市场的测量值流程
Measure-valued processes for energy markets
论文作者
论文摘要
我们介绍了一个框架，该框架允许（非负）测量流程进行能源市场建模，特别是用于电力和天然气期货。将过程的空间结构解释为成熟的时间，我们展示了如何将Heath-Jarrow-Morton方法转化为此框架，从而确保无限维度中的无套利建模。我们得出了一个类似于HJM-Drift条件的类似物，然后在Markovian设置的存在中处理非阴性测量值扩散的扩散。为了分析数学方便的课程，我们在Cuchiero等人上构建。 （2021）并考虑测量值的多项式和仿射扩散，我们可以根据满足某些可接受性条件的连续功能来精确指定扩散部分。为了校准，这些功能可以通过神经网络进行参数化，从而产生神经SPDE的测量值类似物。通过将傅立叶方法或力矩公式与随机梯度下降方法相结合，这允许进行易于处理的校准程序，我们也以市场数据为例测试。我们还概述了如何在可再生能源生产建模的背景下应用测量值的过程。
We introduce a framework that allows to employ (non-negative) measure-valued processes for energy market modeling, in particular for electricity and gas futures. Interpreting the process' spatial structure as time to maturity, we show how the Heath-Jarrow-Morton approach can be translated to this framework, thus guaranteeing arbitrage free modeling in infinite dimensions. We derive an analog to the HJM-drift condition and then treat in a Markovian setting existence of non-negative measure-valued diffusions that satisfy this condition. To analyze mathematically convenient classes we build on Cuchiero et al. (2021) and consider measure-valued polynomial and affine diffusions, where we can precisely specify the diffusion part in terms of continuous functions satisfying certain admissibility conditions. For calibration purposes these functions can then be parameterized by neural networks yielding measure-valued analogs of neural SPDEs. By combining Fourier approaches or the moment formula with stochastic gradient descent methods, this then allows for tractable calibration procedures which we also test by way of example on market data. We also sketch how measure-valued processes can be applied in the context of renewable energy production modeling.
