英文标题：
《Representation of infinite dimensional forward price models in commodity
markets》
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作者：
Fred Espen Benth and Paul Kr\\\"uhner
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最新提交年份：
2014
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英文摘要：
We study the forward price dynamics in commodity markets realized as a process with values in a Hilbert space of absolutely continuous functions defined by Filipovi\\\'c. The forward dynamics are defined as the mild solution of a certain stochastic partial differential equation driven by an infinite dimensional L\\\'evy process. It is shown that the associated spot price dynamics can be expressed as a sum of Ornstein-Uhlenbeck processes, or more generally, as a sum of certain stationary processes. These results link the possibly infinite dimensional forward dynamics to classical commodity spot models. We continue with a detailed analysis of multiplication and integral operators on the Hilbert spaces and show that Hilbert-Schmidt operators are essentially integral operators. The covariance operator of the L\\\'evy process driving the forward dynamics and the diffusion term can both be specified in terms of such operators, and we analyse in several examples the consequences on model dynamics and their probabilistic properties. Also, we represent the forward price for contracts delivering over a period in terms of an integral operator, a case being relevant for power and gas markets. In several examples we reduce our general model to existing commodity spot and forward dynamics.
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中文摘要：
我们研究了商品市场中的远期价格动态，它是一个过程，在Filipovi定义的绝对连续函数的Hilbert空间中具有值。远期价格动态被定义为由无限维Léevy过程驱动的某个随机偏微分方程的温和解。研究表明，相关的现货价格动态可以表示为Ornstein-Uhlenbeck过程之和，或者更一般地表示为某些平稳过程之和。这些结果将可能无限维的正向动力学与经典的商品现货模型联系起来。我们继续详细分析希尔伯特空间上的乘法和积分算子，并证明希尔伯特-施密特算子本质上是积分算子。驱动正向动力学和扩散项的列维过程的协方差算符都可以用这种算符来表示，我们在几个例子中分析了对模型动力学及其概率性质的影响。此外，我们代表一段时间内交付的合同的远期价格，以一个整体运营商为单位，这种情况与电力和天然气市场有关。在几个例子中，我们将通用模型简化为现有的商品现货和远期动态。
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分类信息：

一级分类：Quantitative Finance 数量金融学
二级分类：Pricing of Securities 证券定价
分类描述：Valuation and hedging of financial securities, their derivatives, and structured products
金融证券及其衍生产品和结构化产品的估值和套期保值
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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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