On the No-arbitrage Principle and Option Pricing in a Fuzzy Market

Discuss the no-arbitrage principle in a fuzzy market and present a model for pricing an option. Get a fuzzy price for the contingent claim in a market involving fuzzy elements, whose level set can be seen as the possible price level interval with given belief degree. Use fuzzy densit） function and fuzzy mean as evidence for such model. Also give an example for comparing the result of the model in this article and that of another pricing method.     

Using Binomial Tree Pricing Model in a Fuzzy Market

A model of using binomial tree pricing formulae in a fuzzy market is proposed. In the fuzzy market, a price interval can be got according to the belief degree. The rule for the reasonability of the price interval is proposed. The explicit expression of the interval is discussed in some special settings.     

Stability Analysis of Robust Arbitrage in a Random Interval Valued Financial Market

Stability of robust arbitrage under different probability measures is discussed in a random interval valued financial market.In a fundamental financial market without robust arbitrages, a suitable condition is given to guarantee that the market with new probability measures will also have no robust arbitrage. In order to specify the result got in this article,an example of binomial tree financial model with interval ratios of change is proposed.     

单时期框架下的未定权益定价

文章根据金融数学理论 ,研究单时期框架下未定权益的定价问题。在完全市场下可以仅通过“无套利”的基本原则确定未定权益的唯一价格。在不完全市场下 ,存在未定权益的价格区间。给出了价格区间的性质、估计及其经济意义。     

具有凸多面体不确定性的混杂随机微分方程的镇定分析

研究了带有马尔科夫切换的具有凸多面体不确定性的随机微分方程的稳定化问题。基于离散的系统观测状态设计了反馈控制器,将控制项同时添加在漂移项和扩散项中,使得控制系统均方指数稳定。在控制系统中引入时滞量τ,利用Lyapunov函数方法对控制系统进行分析,得到了使控制系统稳定的反馈控制器满足的条件以及时滞量的确定准则,并以此为理论基础设计控制器,应用线性矩阵不等式方法得到了控制项系数矩阵满足的条件,即微分方程的可镇定判据。具体的数值算例验证了该方法的可行性。     

有交易限制的未定权益定价

讨论了单时期有交易限制的市场背景下未定权益的定价问题。定义了未定权益的买入和卖出保值价格，得到了未定权益的无套利价格区间，说明了价格区间的无套利性质。就一个具体的金融市场模型讨论了所得结论，并分析了限制务件对价格区间的影响。     

On Fair Prices of a Contingent Claim with Random Interval Payoff

In order to get the price of a contingent claim with random interval payoff, a concept of fair price was proposed based on weighted expected utility maximization. After setting up a programming model of maximizing the weighted expected utility involving basic securities and contingent claim,and using techniques in optimization analysis,explicit expressions of the fair price interval for a contingent claim were derived. Relations between acceptable price interval and fair price interval were discussed. It is shown that all fair prices fit the demand for acceptability of a market.     

Option Pricing Method in a Market Involving Interval Number Factors

IntroductionThe classical option pricing methods,Black-Scholespricing model and binomial tree model,give a price of anoption when all key inputs are given as deter ministicquantities.The Black-Scholes option pricing for mula givesthe unique price for a European vanilla option at ti metbased on the underlying stockStwith exercise priceXandexpiration period[t,T]be[1]C=StN(d1)-Xe-r(T-t)N(d2)whered1=ln(St/X)+r+21σ2(T-t)σT-t,d2=d1-σT-tandσis the volatility.In this for mula,the key facto…     

高度非线性比例型混杂随机微分方程的时滞反馈镇定

利用Lyapunov泛函法讨论高度非线性比例型混杂随机微分方程在时滞反馈控制下稳定所需满足的条件.当系数满足局部Lipschitz条件和Khasminskii型条件时,通过设计满足一定条件的时滞反馈控制器构造出适当的时滞量,验证受控后系统存在唯一解且稳定.通过一个算例验证了结论的有效性.