非完全市场衍生资产的相关定价法研究  

Study on correlation pricing formula for derivative assets in incomplete markets

作　　者：陈金龙[1] 张维[2] 

机构地区：[1]华侨大学经济管理学院,福建泉州362011 [2]天津财经学院

出　　处：《系统工程学报》2004年第3期278-283,共6页Journal of Systems Engineering

基　　金：国务院侨办社会科学基金资助项目(02QSK05).

摘　　要：主要研究非完全市场条件下欧式衍生资产的定价问题.利用Hilbert空间的投影理论,首先将Luenberger提出的相关定价法及Bertsimas等人提出的e-套利定价法与向量空间的投影问题联系起来,证明相关定价法与e-套利定价法的一致性及最相关资产的存在性问题,然后利用随机动态规划法研究离散时间和连续时间情形欧式衍生资产的风险对冲策略和定价问题,最后得到确定欧式衍生资产最优风险对冲策略所满足的偏微分方程及相应的近似定价。该微分方程在完全市场条件下与Black＿Scholes方程完全一致.The paper mainly studies the valuation of the European derivative assets in the incomplete market. By applying the theory of orthogonal projection of Hilbert space, the paper first combines the Correlation Pricing Formula presented by Luenberger and e-Arbitrage Approach by Bertsimas, with the projection theory in vector space to prove the identity of the two approaches and the existence of the most correlation asset. Then, with the stochastic dynamic programming approach the paper explores the problems of how to price and hedge the European derivative assets in the setting of discrete and continuous time. Finally, the partial differential equations which the optimal hedging strategy follows and its corresponding approximate price of the assets are obtained. The equation is consistence with the Black-Scholes equation in the complete market.

关 键 词：非完全市场 相关定价法 衍生资产 随机动态规划 

分 类 号：F830.9[经济管理—金融学]