Arbitrage And Pricing In Several Types Of Market With Frictions

It has been known that no-arbitrage is one of the basic hypotheses in the financial research.With the increasing complexity of the economic environment,market friction plays an increasingly important role in financial modeling.How to establish a realistic no-arbitrage pricing principle in the complex and volatile market with frictions has become the top priority of financial research in recent years.In this thesis,no-arbitrage principle and pricing problem are studied in several types of market with frictions,respectively from the perspective of state price vector,equivalent martingale measure and risk-hedging.The fundamental theorem of asset pricing(FTAP)under the corresponding market model is established.In particular,based on the dynamic coherent risk measure,a new approach of pricing independent of martingale measure is given.And the effectiveness of this method is proved by detailed empirical analysis.The details of main work are proposed as follows.1.Excess profit relative to the benchmark asset under?confidence level(?-REP)in a single-period market model with proportional transaction costs is studied.By con-sidering the risk existing in the definition of statistical arbitrage and paying attention to what is a reasonable and fair future return for the investors under a given initial in-put,the concept of?-REP is introduced.The equivalent conditions of non-existence of?-REP are proved,and then the relationships between?-REP,classical strong arbitrage opportunity and strong statistical arbitrage opportunity are discussed.2.Weak no-arbitrage(NA^w)in a multi-period market model with bid-ask spread is studied.Especially,the market is assumed to have two assets,one is risk-free bond and the other is risky asset with the different ask and bid prices.Instead of physical unit,NA^wis defined using the method of liquidation value.A Dalang-Morton-Willinger version of FTAP is established,especially the set of all terminal liquidation values of the self-financing portfolio processes starting from zero is proved to be closed in probability.So that the dual representation of hedging prices of contingent claim is obtained by using Hahn-Banach separation theorem.3.Absence of immediate profits(AIP)in a discrete multi-period market model with incomplete hedging is studied.Allowing the existence of errors in the process of super-hedging contingent claim,the called risk-hedging model is considered based on dynamic coherent risk measure.A weak version of FTAP is established,saying that AIP condition holds if and only if-?_t(S_t+1)?S_t??_t(-S_t+1),(?)t?T-1.Based on the principle of AIP,some characteristics of the minimal super-hedging price are discussed,including the attainment,the time-consistency and the lower and upper bounds;The option pricing with incomplete hedging is studied in a continuous-time market model.The existence and uniqueness of martingale solution of the option pricing equation are proved.4.The pricing of 50ETF call option in Chinese market is studied by choosing dy-namic CVaR as a representative of coherent risk measure.The corresponding results verify the effectiveness of risk-hedging pricing in the discrete-time.