In this paper, we study arbitrage theory in a basic multi-period market model. Malamud and Trubowitz (Math Financ Econ 1(2): 129–161, 2007) used an aggregate state-price deflator and an orthogonal projection onto the payoff subspace to describe the recursive structure of optimal consumption streams. We present explicit expressions of these instruments. We also prove that the density process of a unique minimal martingale measure, with respect to an original measure, can be the aggregate state-price deflator in a market discounted by a numeraire.

中文翻译：

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多期市场模型中的总状态价格平减指数

在本文中，我们在一个基本的多周期市场模型中研究套利理论。Malamud 和 Trubowitz（Math Financ Econ 1(2): 129–161, 2007）使用汇总状态价格平减指数和对收益子空间的正交投影来描述最优消费流的递归结构。我们展示了这些工具的明确表达。我们还证明了一个独特的最小马丁格尔测度的密度过程，相对于一个原始测度，可以是一个被计价器贴现的市场中的总状态价格平减指数。