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摘要翻译：
本文并不先验地假定金融资产价格的演化是半线性的。由于投资者的可能策略是自负盈亏的，所以以前的价格被迫是有限的二次变化过程。如果允许策略的类$\mathcal{A}$受到限制，则不排除非套利性质。用$\mathcal{A}$-鞅的概念代替了经典鞅的概念。给出了一个与$\Mathcal{A}$-鞅有关的微积分，并给出了一些例子。扩展了无套利、生存能力、套期保值和内部人效用最大化的一些应用。最后讨论了Bender-Sottinen-Valkeila型无套利条件。
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英文标题：
《On stochastic calculus related to financial assets without
semimartingales》
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作者：
Rosanna Coviello (LAGA), Cristina Di Girolami (ENSTA ParisTech, Luiss
Guido Carli), Francesco Russo (ENSTA ParisTech, INRIA Rocquencourt)
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最新提交年份：
2011
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分类信息：
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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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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英文摘要：
This paper does not suppose a priori that the evolution of the price of a financial asset is a semimartingale. Since possible strategies of investors are self-financing, previous prices are forced to be finite quadratic variation processes. The non-arbitrage property is not excluded if the class $\mathcal{A}$ of admissible strategies is restricted. The classical notion of martingale is replaced with the notion of $\mathcal{A}$-martingale. A calculus related to $\mathcal{A}$-martingales with some examples is developed. Some applications to no-arbitrage, viability, hedging and the maximization of the utility of an insider are expanded. We finally revisit some no arbitrage conditions of Bender-Sottinen-Valkeila type.
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PDF链接：
https://arxiv.org/pdf/1102.2050
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