股票价格服从跳跃-扩散过程套期保值问题的随机LQ框架

Stochastic LQ Control EYamework for the Hedging Problem as the Stock Price Follows Jump-diffusion Process

在连续时间金融模型中,一般认为股票(风险资产)的价格的随机扰动为标准的Brown运动,然而在现实中,当有重大信息出现时会对股票的价格产生冲击,使其呈现不连续的跳跃,即股票价格表现为一种跳跃-扩散过程,文中将随机LQ控制模型推广到系统状态的跳-扩过程的随机LQ控制,通过引入跳-扩的Riccati方程而得到最优的反馈控制,然后,运用该框架去处理金融中未定权益的套期保值问题,得到了最优套期保值策略。

In continuous time finance model the stock price volatility is assumed to follow the Brownian motion. However in real world as the significant information occurs, the stock price has discontinuous jump. This paper extends the classical stochastic LQ control to the jump-diffusion model and the jump-diffusion stochastic Riccati equation is introduced, the optimal feedback control can be obtained. As an application in hedging strategy, we obtain the optimal hedging strategy.