基于效用的集合理财产品定价  

Pricing Collective Financing Products Based on Utility

作　　者：杨招军[1] 黄冰华[1] 

机构地区：[1]湖南大学金融与统计学院,湖南长沙410079

出　　处：《系统工程》2013年第6期54-58,共5页Systems Engineering

基　　金：国家自然科学基金资助项目(70971037;71171078);教育部博士点基金资助课题(20100161110022)

摘　　要：考虑到市场非完备和投资者风险厌恶的实际情形,本文基于效用无差别定价原理,利用随机控制方法,得到集合理财产品价格满足的偏微分方程,运用有限差分法进行数值分析。结果表明:当风险厌恶系数增加时,集合理财产品效用无差别价格随着产品封闭期延长先升后降;风险态度仅通过产品的非系统风险影响产品价格;若理财产品与市场相关性越弱(强),则风险态度对价格影响越大(小),特别地,若二者完全相关,即非系统风险为零,风险态度不对价格产生影响;产品价格是固定管理费率和超额收费率的递减的凸函数。Taking into account that markets are actually incomplete and investors are risk-averse, based on Undifferentiated Utility Pricing Principle, we get a partial differential equation satisfied by the price of collective financing products according to stochastic control principle. We provide numerical solutions by finite difference methods. The results show that, when risk aversion coefficient increases, the undifferentiated utility price of the financial product first increases, then decreases as the lifetime of the product increases. The risk attitude of an investor affects the product＇s price only via the non-systematic risk of the product： The weaker （stronger） the correlation between the product and the market, the larger （smaller） the risk attitudes impose an influence on the products＇ price. Especially, if both of them are completely correlated, i.e. non-systematic risk is zero, and the products＇ price is independent of the risk attitudes. The products＇ price is a decreasing and convex function of both the fixed management fee rate and the excess fee rate.

关 键 词：投资理论 集合理财产品 效用无差别原理 保底条款 非系统风险 

分 类 号：F830[经济管理—金融学]