Friction (a, B) Of The Market - No-arbitrage Theory And Characteristics Of The Study

It is well known that a balanced financial market can be essentially portrayed by the arbitrage principle. Since it was perceived by people, it has been an enduring topic in the field of financial economics.In recent years, the research of no-arbitrage theory and its application are most focused on the frictional market. Researchers use optimization theory, convex separation theorem and other mathematical methods to depict no-arbitrage definition and theories of frictional market. For example, the no-arbitrage research in a single finite state model that there exist bid-ask spread and proportional transaction costs and so on.This article intends to carry out a similar study. After analysis and exploration of the classic no-arbitrage theory deeply, We put forward the (a,b)-no arbitrage model, the (a,b)-no arbitrage model based on the lever of a and describe their characteristics in the frictional market.Firstly, we give the definition of (a.b)-no arbitrage,(a,b)-strong no arbitrage and (a,b)-weak no arbitrage.Secondly, we use the optimization theory, convex separation theorem, the dual problem and so on to characterize the (a.b)-strong no arbitrage market and (a,b)-weak no arbitrage market.Finally, in this article, we give the definition of (a,b)-no arbitrage based on the lever of a and construct the almost (a,b)-no arbitrage model. We also give some basic characteristics under the almost (a,b)-no arbitrage model.The results obtained in this paper can be regarded as a natural generalization to the classic (a,b)-no arbitrage principle. These conclusions are also benefit for the further research of almost (a,b)-no arbitrage market.