Research On (a,b)-No Arbitrage -Under Friction Market With Transaction Fee

Since the hypothesis of "No-Arbitrage Equilibrium" is put forward, finance has stepped into a "quantitative" stage from the "qualitative" stage as an independent branch of economics. Therefore, it is important to study the significance and application value of No-Arbitrage Theory, which contributes to fully grasp the connotation of modern finance and improve the comprehensive understanding of the modern financial system.For a long time, the study of no-arbitrage in friction market is based on the breakthrough point that "if the initial investment is zero, the final yield is also zero". Starting from the perspective of the practical significance, this dissertation studies the problem that "what is the minimal initial investment a if the contingent claim is b(≠ 0)". Following meaningful results are obtained.Firstly, this dissertation studies no-arbitrage in friction market with proportion transaction fee. A numerical solution of (a, b)-No-Arbitrage model is worked out using G-PPA, which indicates the existence of(a, b)-No-Arbitrage. What’s more, some new characterizations of (a, b)-Strong (Weak)-No-Arbitrage are provided by the variational technology and the theory of convex analysis. At the same time, the stability related to the revenue matrix R and Robust stability related to a martingale price measure P of (a,b)-No-Arbitrage are proved in complete market with no redundancy.Secondly, this dissertation studies no-arbitrage in friction market with fixed transaction fee and proportion transaction fee. The new definitions of (a,b)ω-No-Arbitrage and (a,b)ω-Strong-No-Arbitrage are put forward and their equivalency are proved. Then this dissertation provides characteristics of (a, b)ω-Strong-No-Arbitrage and (a, b)ω-No-Arbitrage using the theory of convex analysis. The relationship between optimal consumption and (a,b)ω-No-Arbitrage is given through the optimal consumption problem. At the same time, this dissertation proves the equivalency between (a,b)-Strong-No-Arbitrage and (a,b)ω-Strong-No-Arbitrage.All results of this dissertation, which can be regarded as reasonable extensions of classic No-Arbitrage Theory, have reference value for further researches in this field.