论文标题
向后堆叠式差异游戏具有约束：混合终端扰动和线性季度方法
Backward Stackelberg Differential Game with Constraints: a Mixed Terminal-Perturbation and Linear-Quadratic Approach
论文作者
论文摘要
我们讨论一个涉及单个领导者和单一追随者的开环向后堆场差异游戏。与大多数Stackelberg游戏文献不同，要控制的状态的特征是向后的随机微分方程（BSDE），该方程（BSDE）为终端 - 而不是初始条件指定为先验。领导者的决定包括静态终端扰动和动态线性季度控制。另外，终端控制受到（凸封）的（凸置）方向和（仿射）期望约束。两种约束都是由数学金融等实际应用产生的。有关信息模式：领导者在初始时间宣布终端和开环动态决策，同时考虑了追随者的最佳响应。然后，通过追随者（向后线性 - 季节（BLQ）问题）和领导者（混合终端扰动和向后向前进的LQ（BFLQ）问题）顺序解决了两个相互关联的优化问题。我们的开环stackelberg平衡由一些具有混合初始末端条件的向后耦合的后方随机微分方程（BFSDE）表示。我们的BFSDE还涉及非线性投影操作员（由于点的约束）与Karush-Kuhn-Tucker（KKT）系统（由于期望约束）通过Lagrange乘数结合使用。在某些非平凡的情况下，还讨论了此类BFSDE的全球可溶性。我们的结果应用于一个财务示例。
We discuss an open-loop backward Stackelberg differential game involving single leader and single follower. Unlike most Stackelberg game literature, the state to be controlled is characterized by a backward stochastic differential equation (BSDE) for which the terminal- instead initial-condition is specified as a priori; the decisions of leader consist of a static terminal-perturbation and a dynamic linear-quadratic control. In addition, the terminal control is subject to (convex-closed) pointwise and (affine) expectation constraints. Both constraints are arising from real applications such as mathematical finance. For information pattern: the leader announces both terminal and open-loop dynamic decisions at the initial time while takes account the best response of follower. Then, two interrelated optimization problems are sequentially solved by the follower (a backward linear-quadratic (BLQ) problem) and the leader (a mixed terminal-perturbation and backward-forward LQ (BFLQ) problem). Our open-loop Stackelberg equilibrium is represented by some coupled backward-forward stochastic differential equations (BFSDEs) with mixed initial-terminal conditions. Our BFSDEs also involve nonlinear projection operator (due to pointwise constraint) combining with a Karush-Kuhn-Tucker (KKT) system (due to expectation constraint) via Lagrange multiplier. The global solvability of such BFSDEs is also discussed in some nontrivial cases. Our results are applied to one financial example.
