We study general undiscounted asset price processes, which are only assumed to be nonnegative, adapted and RCLL (but not a priori semimartingales). Traders are allowed to use simple (piecewise constant) strategies. We prove that under a discounting-invariant condition of absence of arbitrage, the original prices discounted by the value process of any simple strategy with positive wealth must follow semimartingales. We also establish a corresponding version of the fundamental theorem of asset pricing that involves supermartingale discounters with an additional strict positivity property.

中文翻译：

---

适当打折的资产价格属于半成品

我们研究了一般的未折现资产价格过程，这些过程仅假定为非负的，适应性的和RCLL（但不是先验半市场）。允许交易者使用简单的（分段常数）策略。我们证明，在没有套利的贴现不变条件下，通过任何具有正财富的简单策略的价值过程所贴现的原始价格必须遵循半mart态。我们还建立了资产定价基本定理的相应版本，其中涉及具有额外严格正性的超级市场折扣店。