ABSTRACT

For the potential applications in uncertainty problems, risk measures and superhedging problems in finance, the theory of nonlinear expectation attracts researchers’ great interest. Base on G-expectation, in this work, we discuss the stabilisation issue for a class of stochastic multi-group models driven by G-Brownian motion (G-MGMs, in short) via delay feedback control design. By employing the concept of graph theory and G-Lyapunov approach, we establish both Lyapunov criteria and coefficient-type criteria for guaranteeing the stabilisation of the addressed model. Further, a class of stochastic coupled oscillators driven by G-Brownian motion is discussed. Finally, an example is offered to verify the validity of the obtained theoretical results.

摘要

对于金融中的不确定性问题、风险测度和超级对冲问题的潜在应用，非线性期望理论引起了研究人员的极大兴趣。基于G-期望，在这项工作中，我们通过延迟反馈控制设计讨论了一类由G-布朗运动（简称G- MGMs）驱动的随机多组模型的稳定性问题。通过运用图论的概念和G -Lyapunov方法，我们建立了Lyapunov准则和系数类型准则，以保证所寻址模型的稳定性。此外，一类由G驱动的随机耦合振荡器- 讨论布朗运动。最后，通过实例验证了所得理论结果的有效性。