能源市场的前向动力学——无限维建模与仿真

Pub Date : 2014-10-24 DOI:10.1080/17442508.2014.895359
A. Barth, F. Benth
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引用次数: 18

摘要

本文介绍了一种无限维的能源期货市场模型。与利率模型中的Heath-Jarrow-Morton框架类似,一阶双曲型随机偏微分方程模拟了远期价格曲线的动态。对这些方程进行了分析,特别研究了由无穷维鞅过程驱动的随机偏微分方程在一般情况下的正则性和无套利条件。研究了电力期货合约的算术和几何价格动态,并对交割期进行了计算。介绍了双曲型随机偏微分方程的稳定收敛的有限元数值逼近方法,并将其应用于与能源市场相关的一些实例。
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The forward dynamics in energy markets – infinite-dimensional modelling and simulation
In this paper an infinite-dimensional approach to model energy forward markets is introduced. Similar to the Heath–Jarrow–Morton framework in interest-rate modelling, a first-order hyperbolic stochastic partial differential equation models the dynamics of the forward price curves. These equations are analysed, and in particular regularity and no-arbitrage conditions in the general situation of stochastic partial differential equations driven by an infinite-dimensional martingale process are studied. Both arithmetic and geometric forward price dynamics are studied, as well as accounting for the delivery period of electricity forward contracts. A stable and convergent numerical approximation in the form of a finite element method for hyperbolic stochastic partial differential equations is introduced and applied to some examples with relevance to energy markets.
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