A Commodity Price Process with a Unique Continuous Invariant Distribution Having Infinite Mean
提出一种可储存商品的价格模型,其价格过程不同于传统农产品或耗竭性资源模型,具有零产出正概率、价格无穷大、预期价格和方差趋于无穷、价格必然有限时间内下降、储存始终为正、预期消费有正下界等特征,并存在一个均值无穷的连续不变分布。
We present a model of a storable commodity with a price process different from those usually associated with agricultural commodities or exhaustible resources. This model has positive probability of zero output. For consumption equal to zero, price is infinite. In any initial period with finite price, the path of expected prices, conditional on current information, approaches infinity at a rate determined by the cost of storage, and the variance also approaches infinity. Price is expected to fall with probability one in finite time. Successive price realizations are always correlated, storage remains strictly positive, and expected consumption exceeds a strictly positive bound. There is a continuous limiting invariant distribution of price, with infinite mean.