基于鲁棒控制的期权套期保值策略

Option Hedging Strategy Based on Robust Control

在标的资产价格服从带有随机方差几何布朗运动的非完全市场假设条件下 ,应用随机微分对策方法 ,研究与标的资产有关的欧式期权的动态套期保值策略问题。建立了最优动态套期保值策略的随机微分对策数学模型 ,给出了基于鲁棒控制的均方复制误差最小的自融资动态套期保值策略。当方差为时间的确定性函数时 ,最优动态套期保值策略与用 Black- Scholes套期比表示的

The dynamic hedging problem for European options is studied by applying stochastic differential game method, under the assumption of incomplete market where the underlying assets prices follow geometric Brownian motion with stochastic volatility. The stochastic differential game model for the self financing hedging strategy is estabilished. A dynamic hedging portfolio that yields the minimum mean square replication error is given. When the volatility is a deterministic function of time, the strategy coincides with Black Scholes's delta hedging.