复杂摩擦金融市场中的弱无套利分析

An Analysis of Weak No-arbitrage in a Friction Compicates Market

在金融工程的研究中,无套利分析被证明是非常重要的工具。套利通常定义为在无风险下的获利机会,在常态下,经济学家认为套利是不存在的(至少不是对任何一段时间来说),相应地,在经济和金融数学的研究中,无套利假说就成为一个基本的原则。在各种文献中,无套利越来越受到更多的关注,例如Ardalan(1999),Jouini和Kallar(1995),Prisman(1986)、Li和Wang(2001),Deng、Li和Wang(2000)等。在金融中一个重要的基础性的结果是无套利条件的等价性和在无交易费用市场价格系统的存在性(Ross,1978),Garmanand、Ohlson(1981)把该结果推广到成比例的交易费用市场情况,Dermody和Prisman(1993)进一步推广该结果到包括投资者市场影响和卖空费用的交易费情况。本文分析了金融市场中包括两种不同的固定交易费、不成比例的交易费和买卖价差及税收等条件下的弱无套利的情形,运用优化理论和凸分析方法,得到弱无套利的一些重要性质。

No-arbitrage has been proven to be a very important tool in the study of financial engineering. Arbitrage is commonly defined as a profit-making opportunity at no risk. Economic states with arbitrage are believed not to exist（ at least not for any signifciant duration of time）in a normal situation, accordingly,no-arbitrage assumption has been a fundamental principal in the studies of mathematical economics and finance. No-arbitrage has received much attention in the literature,for exemple, Carassus,Pham,and Touzi（2001 ） and Ardalan（ 1999）, Jouini and Kallar（ 1995 ）, Prisman（ 1986）, Li and Wang（2001 ） and Deng, Li and Wang（2000）. One of the fundamental results in finance is the equivalence between no-arbitrage condition and existence of a pricing operator in markets with no transaction （see Ross ,1978）. Garmanand and Ohlson （1981）extended this result to markets with proportional transaction costs . Dermody and Prisman （1993） extended the result to a transaction costs that include the investor＇ market-impact and short-borrowing costs. Furthermore, No-arbltrage in a Frictional Market. For a finlte-security and finite-state financial market with three forms of friction ： ask-bid spread, transaction costs and tax, by using the theory of convex analysis and some optimization techniques, a series of necessary and sufficient conditions are established to characterize weak . In particular, the existence of a semi-positive solution or a strictly positive solution to a linear inequality system is used to characterize weak. It makes one to find if there exists an arbitrage opportunity in the frictional market by a linear programming algorithm in polynomial time. This might be a fundamental result in computational finance. （See Li ,2002）. In this paper we study the characterization in a friction compicates where the transaction costs include two difference fixed costs,a proportional costs and bid-ask spreads,and tax. These assumptions make us more realistic than these previously studies. On the other hand ,these assumptions make cost function become more complicated. In word, by using convex analysis and optimization theory, a series of results are derived , It＇s results make us more realistic and extend many results known in some existing literature.