垂直投影与非完全市场条件下的衍生资产定价

Orthogonal projection and the derivatives asset pricing under incomplete market

利用垂直投影理论确定非完全市场条件下,标的资产价格遵循鞅过程的衍生资产最优风险对冲策略,然后通过扩展投影理论,研究基于标的资产及其衍生资产价格信息的资产定价与风险对冲问题,得到最优混合交易策略和该衍生资产的近似市场定价.

Firstly, the paper applies the theory of orthogonal projection to solve the optimal hedging strategy of derivative asset under the incomplete market, with the assumption that the price process of the underlying asset is martingale. Then, by the way of extending orthogonal projection, the paper explores the problems of how to price and hedge the derivative asset, based on the knowledge of market price information of underlying asset and other assets. Finally, the optimal hedging mixed portfolio strategy and its corresponding approximate price of the assets are obtained.