Stochastic control of Levy driven processes with application to mathematical finance

我们提出了一种求解levy驱动随机微分方程弱逼近的优化方法，这是许多实际应用的一般形式。我们采用数学规划框架来获得目标的数值上界和下界估计。我们的方法的一个优点是我们不需要生成样本路径。通过对数学金融的应用验证了该方法的有效性。我们还从各个方面研究了随机控制系统的分析/设计，例如随机噪声下超大规模复杂网络共识动力学的鲁棒性。

We proposed an optimization approach to weak approximation of Levy-driven stochastic differential equations, which is a general form of many practical applications. We employ a mathematical programming framework to obtain numerically upper and lower bound estimates of the target. An advantage of our approach is that we do need no sample path generation. The effectiveness was verified through an application to mathematical finance. We also investigated analysis/design of stochastic control systems from various aspects, such as robustness of consensus dynamics overlarge-scale complex networks under stochastic noise.