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摘要翻译：
本文给出了金融市场中离散时间交易的一个随机模型，其中交易成本由凸成本函数给出，投资组合由凸集约束。该模型不假设存在现金账户/数字单位。除了经典的无摩擦市场和有交易费用或买卖价差的市场外，我们的框架还涵盖了具有大量瞬时交易的非线性非流动性效应的市场。在存在非线性的情况下，套利的经典概念被证明有两个同样有意义的推广，一个边际的推广和一个可扩展的推广。通过分析描述成本函数和约束的局部和全局行为的两个辅助市场模型，我们研究了它们与状态价格平减指数的关系。
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英文标题：
《Arbitrage and deflators in illiquid markets》
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作者：
Teemu Pennanen
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最新提交年份：
2009
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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：Functional Analysis 功能分析
分类描述：Banach spaces, function spaces, real functions, integral transforms, theory of distributions, measure theory
Banach空间，函数空间，实函数，积分变换，分布理论，测度理论
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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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英文摘要：
This paper presents a stochastic model for discrete-time trading in financial markets where trading costs are given by convex cost functions and portfolios are constrained by convex sets. The model does not assume the existence of a cash account/numeraire. In addition to classical frictionless markets and markets with transaction costs or bid-ask spreads, our framework covers markets with nonlinear illiquidity effects for large instantaneous trades. In the presence of nonlinearities, the classical notion of arbitrage turns out to have two equally meaningful generalizations, a marginal and a scalable one. We study their relations to state price deflators by analyzing two auxiliary market models describing the local and global behavior of the cost functions and constraints.
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PDF链接：
https://arxiv.org/pdf/0807.2526
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