We have embedded the classical theory of stochastic finance into a differential geometric framework called Geometric Arbitrage Theory and show that it is possible to:
--Write arbitrage as curvature of a principal fibre bundle.
--Parameterize arbitrage strategies by its holonomy.
--Give the Fundamental Theorem of Asset Pricing a differential homotopic characterization.
--Characterize Geometric Arbitrage Theory by five principles and show they they are consistent with the classical theory of stochastic finance.
--Derive for a closed market the equilibrium solution for market portfolio and dynamics in the cases where:
-->Arbitrage is allowed but minimized.
-->Arbitrage is not allowed.
--Prove that the no-free-lunch-with-vanishing-risk condition implies the zero curvature condition.
No-arbitrage in discrete-time markets with proportional transaction costs and general information structure
本文在一般信息结构下讨论了具有比例交易费用的离散金融市场模型的无套利条件。我们将Kabanov and al.（2002）、Kabanov and al.（2003）和Schachermayer（2004）的结果推广到买卖价差不确定的情况。在“无摩擦”的情况下，我们恢复Kabanov和Stricker（2003）的结果。
On free lunches in random walk markets with short-sale constraints and small transaction costs, and weak convergence to Gaussian continuous-time processes
