中文摘要：

在经典的完全市场中，根据无套利原理，能够为期权提供唯一的价格同时可以完全对冲风险．在这样的理论假设下，没有理由管理不好相关衍生产品的风险．但是在现实的金融市场中，有关衍生产品风险管理失败的案例时有发生，特别是最近的金融危机使人们认识到，现实的金融市场是非常复杂而不完全的．在这样的市场中，风险不能完全对冲，定价与对冲问题也变得不易处理，至今还没有一致接受的理论．为了促进更深入的研究，综述了各种在不完全市场中的定价与对冲方法，侧重于基本思想和基本模型．同时也探讨了各种方法的优缺点，以及它们之间的联系，突出了优化理论和方法在解决这类问题中的关键作用，同时也分析了一些需要进一步研究的问题及方法上的空白点．

英文摘要：

In the classical complete finance market, we can provide the unique price for option according to arbitrage-free principle and we can also hedge risk perfectly. With such a hypothesis, we can manage the risk of derivatives efficiently and easily. But in the realistic finance market, many poor risk management cases happen frequently. And the current finance crisis show that the realistic finance market is very complicated and incomplete. In incomplete market, the risk can not be hedged away perfectly, and pricing and hedging problems are intractable. There is no consistent acceptable theory. In this paper, we survey various methods of pricing and hedging in incomplete market for promoting further investigation. We focus on the basic ideas and basic models, and explore the advantages and drawbacks of these methods and the relationship between them. We emphasise the key role that the optimization theory and methods will play and in the meanwhile we also analyse some problems and the gaps in methods that need to make further investigation.