Itô Calculus without Probability in Idealized Financial Markets*
Itô Calculus without Probability in Idealized Financial Markets*
复制标题
理想化金融市场中没有概率的伊藤微积分*
DOI：
10.1007/s10986-015-9280-1
复制
发表时间：
2011
影响因子：
0.4
通讯作者：
V. Vovk
中科院分区：
文献类型：
--
作者：
V. Vovk
我们考虑理想化的金融市场，其中交易证券的价格路径是càdlàg函数，对允许的跳跃大小施加了适度的限制。我们证明了典型的价格路径的二次变化的存在，其中的资格“典型”的意思是，有一个交易策略，风险只有一个货币单位，并带来无限的资本，如果二次变化不存在。这一结果允许一个应用许多已知的结果在路径伊藤演算典型的价格路径，我们给出了一个简要的概述，这样的结果。
We consider idealized financial markets in which price paths of the traded securities are càdlàg functions, imposing mild restrictions on the allowed size of jumps. We prove the existence of quadratic variation for typical price paths, where the qualification “typical” means that there is a trading strategy that risks only one monetary unit and brings infinite capital if quadratic variation does not exist. This result allows one to apply numerous known results in pathwise Itô calculus to typical price paths; we give a brief overview of such results.