Portfolio Changes In Transaction Rates And Arbitrage Pricing

In the frictional market, contingent claims usually can't be completely hedged, and this hedging problem can be regarded as a portfolio problem. Recently, people are studying the portfolio problem under the frictional market, but just study the problem of the fixed rate of transaction costs. As far as we know, the research about the variable rate is still open.First of all, this paper poses a jump rate of transaction costs according to the real market, and based on this, we get an optimal model of minimizing risk. For this model, we use the Calculus of Variation to prove the existence of the optimal strategy.Second, we make a study of no-arbitrage pricing theory when the market is associated with jump-transaction costs, and obtain a binomial pricing formula. This result generalizes the binomial pricing formula without transaction costs.