有交易费的未定权益无套利公平定价

No-arbitrage fair pricing of contingent claims under transaction costs

讨论了有交易费市场模型下未定权益无套利公平定价问题 .首先 ,提出了资产折算函数 .其次 ,基于资产折算函数并利用辅助鞅方法 ,给出了在有交易市场模型下套利机会的定义和无套利分析的一些结果的讨论 .第三 ,借助微分方程和价值函数的方式 ,给出了有交易费市场模型下未定权益无套利公平价的定义 .最后 ,利用随机分析和无套利分析的理论 ,给出了有交易费市场模型下未定权益的上、下无套利公平定价形式 .这样 ,即可以给出有交易费市场模型下未定权益无套利公平定价区 ,同时 ,还给出了在风险资产不参与交易下 。

A reasonable fair pricing of the contingent claims was discussed for the given market model under transaction costs.First,the discount asset function on the model was put forward.Then based on the discount asset function,the definition of arbitrage opportunities was introduced for the given market model under transaction costs,and some results about the arbitrage-free analysis were given by using the methods of auxiliary martingales and the discount asset function.By using the fashions of differential equation and the value functions of the assets,the definition of arbitrage-free fair pricing of the contingent claims was given under the market model.Finally, by means of the theories of the stochastic analysis and the arbitrage-free analysis, the super arbitrage-free fair pricing and inferior arbitrage-free fair pricing of the contingent claims were given for the given market model.Thus,the arbitrage-free fair pricing interval of the contingent claims was appropriately given for the given market model under transaction costs.At the same time,a special arbitrage-free fair pricing formula was also given while the risk assets were not traded under the given market model.