The Convex Analysis And Optimization Theory With Several Applications In The No-arbitrage Analysis In The Complicated Friction Market

No-arbitrage has proven to be a very important tool in the study of financial engineering. Arbitrage is commonly defined as a profit-making opportunity at no risk . Economic states with arbitrage are believed not to exist(at least not for any signifciant duration of time)in a normal situation.accordingly,no-arbitrage assumption has been a fundamental principal in the studies of mathematical economics and finance.No-arbitrage has received much attention in the literature, See for exemple, Carassus,Pham,and Touzi(2001) and Ardalan(1999), Jouini and Kallar(1995), Prisman(1986), Li and Wang(2001) and Deng,Li and Wang(2000).One of the fundamental results in finance is the equivalence between no-arbitrage condition and existence of a pricing operator in markets with no transaction (see Ross ,1978).Garmanand and Ohlson (1981)extended this result to markets with proportional transaction costs .Dermody and Prisman (1993) further extended the result to a transaction costs that including the investor' market —impact and short-borrowing costs.In this paper we consider a frictional financial market where the transaction costs includes two difference fixed costs,a proportional costs and bid-ask spreads,and tax.there assumptions make our model more realistic than there previously studied.On the other hand,there assumptions make cost function become more complicated.In word, By using convex analysis and optimization theory,We study characterization of in a friction compicates.It' reault make our model more realistic.In section 2 we analyse the structure of interest rates in markets with transaction costs including bid-ask spreads, a proportional costs, tax, two difference fixed costs,Applying methodologies in optimization theory and convex analysis,several necessary and sufficient condition are derived for the term structure of interest rates.In section 3. we study characterization of strong and weak no-arbitrage in a friction compicates market. We also study an optial consumption-portfolio selection problem in a friction complicate market.By using convex analysis and optimization theory,a series of results are derived .these results extend many results known in some existing literature.In section 4. By using the methods of auxiliary and convex analysis,we also achieve a series of new results.