On The Problem Of Robust Dominant Strategy And Robust Arbitrage Opportunity In The Random Market Model With Parameter

With the development of financial market, uncertainty in the market is more and more significant. This paper puts forward a composite and financial market model influenced by random and subjectivity, and researches on some problems in the random income financial markets with parameter. In the market, the security payoffs was described by a random variables with parameter. The random variables with parameter not only reflects the uncertainty of future market state, but also covers the possible range of the security price under each future state. This paper works on the two problems of robust dominating strategy and robust arbitrage opportunity in the random income financial markets with parameter under one period setting.This paper works on the analysis of robust dominant strategy and robust ar-bitrage opportunity in the random income financial markets with parameter. We introduce the random income financial markets with parameter. In the market, the probability of space frame of the finite dimension is extended to the general prob-ability space. Some concepts, such as robust dominant strategy, robust arbitrage opportunity, acceptable linear pricing measures and acceptable risk-neutral pricing measures, are given and discussed parallel to those in traditional market analysis. With these new concepts, it is discussed that the requirement of nonrobust dom-inant strategy is equivalent to the existence of acceptable linear pricing measures and nonrobust arbitrage opportunity is equivalent to the existence of acceptable risk-neutral pricing measures. Then we discuss the relations between the analysis of the nonrobust dominant strategy in the random income financial markets with parameter and its in traditional market and the relations between robust dominant strategy and robust arbitrage opportunity.Noticing that the random income financial markets with parameter is the ex-tension of the traditional market, the discussion of the propositions is based on the analysis of dominant strategy and arbitrage opportunity. We get many meaningful conclusions. We also find that the results in the random income financial markets with parameter contain those in the traditional market. Therefore, it is obvious that in the random income financial markets with parameter is the meaningful extension of the traditional market. Not only does the former include more information and uncertainty, but also it is closer to real market.