With Convex Friction Of Transaction Costs Market Arbitrage Asset Pricing

The asset pricing of no-arbitrage has always been one of important topics in finance, and there are many research results.In recent years, scholars focus their attention on the issue of asset pricing with the proportional transaction costs in single and multi-period securities market, and have given its model of the no-arbitrage asset pricing. However, as far as we known, the results of no-arbitrage asset pricing theory with convex transaction costs for the multi-period securities market and the possible further expansion for the "no-arbitrage principle" are relatively small. These two topics mainly will be studied in this paper.Firstly, the "almost no-arbitrage pricing" model is defined as an extension of the classical no-arbitrage principle, and some properties of "almost no-arbitrage model" are obtained here.Secondly, the paper is to promote a single period asset pricing theory of no-arbitrage with convex transaction costs function to the multi-period securities market, and to give the corresponding conclusion which is similar to the result where the transaction costs function is proportional by the separating theorem of convex set and some knowledge about the sub-differential.These results posed in this paper are new and have certain economic significance. Among, the partial results can be regarded as a natural extension for the existed asset pricing theory of no-arbitrage.