Asymptotic arbitrage with small transaction costs
Asymptotic arbitrage with small transaction costs
复制标题
交易成本较小的渐近套利
DOI：
10.2139/ssrn.2560176
复制
发表时间：
2013
影响因子：
1.7
通讯作者：
Lavinia Perez
中科院分区：
文献类型：
--
作者：
I. Klein;E. Lépinette;Lavinia Perez
利用λ n-相容价格系统诱导的等价概率测度序列的连续性，给出了在市场n上具有小比例交易费用λn的金融市场序列的第一类、第二类渐近套利和强渐近套利的刻画.这些结果类似于无摩擦的情况;比较（Kabanov和Kramkov在Finance Stoch. 2：143-172，1998; Klein和Schachermayer in Theory Probab. 41：927-934，1996）。我们的设置很简单，每个市场n包含两个资产。证明使用定量版本的哈尔莫斯-萨维奇定理（见克莱因和Schachermayer在安。24：867-881，1996）和非负局部鞅的单调收敛结果。此外，我们还研究了市场n上无交易费用但交易费用λn>0的强渐近套利模型的例子，不存在任何形式的渐近套利。在一种情况下，（λn）甚至可以收敛到0，但不会太快。
We give characterizations of asymptotic arbitrage of the first and second kind and of strong asymptotic arbitrage for a sequence of financial markets with small proportional transaction costs λn on market n, in terms of contiguity properties of sequences of equivalent probability measures induced by λn-consistent price systems. These results are analogous to the frictionless case; compare (Kabanov and Kramkov in Finance Stoch. 2:143–172, 1998; Klein and Schachermayer in Theory Probab. Appl. 41:927–934, 1996). Our setting is simple, each market n contains two assets. The proofs use quantitative versions of the Halmos–Savage theorem (see Klein and Schachermayer in Ann. Probab. 24:867–881, 1996) and a monotone convergence result for nonnegative local martingales. Moreover, we study examples of models which admit a strong asymptotic arbitrage without transaction costs, but with transaction costs λn>0 on market n; there does not exist any form of asymptotic arbitrage. In one case, (λn) can even converge to 0, but not too fast.