证券组合优化模型的随机LQ控制框架

Stochastic LQ control framework and its applicaiton in finance as the stock price follows the jump-diffusion process

将随机LQ控制模型推广到系统状态为跳跃 扩散过程的随机LQ控制,通过引入跳跃 扩散的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,与均值 方差分析模型,得到了精确的最优套期保值策略与最优的投资组合策略.

In the continuous time finance model the stock price volatility is deemed the Brownian motion. However in the real world as the significant information occurs, a discontinuous jump will occur in the stock price. This paper extends the classical stochastic LQ control to the jump-diffusion model. With the jump-diffusion stochastic Riccati equaiton introduced, the optimal feedback control can be obtained. With its application in hedging strategy and the Mean-Variance model, we obtain the optimal hedging strategy and the optimal portfolio strategy.