全耦合非线性正倒向随机差分方程：谱压缩与无穷时域最大值原理
Fully Coupled Nonlinear Forward-Backward Stochastic Difference Equations: Spectral Contraction and Infinite-Horizon Maximum Principle
- Fudan University（复旦大学）
- Shandong University（山东大学）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
本文提出显式谱压缩方法，研究无穷时域全耦合非线性正倒向随机差分方程，推导随机最大值原理及验证定理，并用投资组合示例展示应用。
AI中文摘要：
本文发展了一种显式谱压缩方法，用于研究无穷时域上的全耦合非线性正倒向随机差分方程及其在随机控制中的应用。该全耦合系统的估计被组装成一个显式的二维非负矩阵。其谱半径给出了一个显式的充分贴现阈值，并构造了相应的等价加权乘积范数以建立压缩性质。此外，对于具有凸控制约束和累积贴现运行成本的无穷时域控制问题，我们推导了Pontryagin型随机最大值原理、其等价的逐点法锥表述以及一个验证定理。最后，给出了一个递归风险调整的投资组合示例，以展示我们理论结果的应用，并推导了该示例的投影型充分最优性条件。
英文摘要：
This paper develops an explicit spectral-contraction approach to studying fully coupled nonlinear forward--backward stochastic difference equations on infinite horizon and their applications to stochastic control. The estimates for this fully coupled system are assembled into an explicit two-dimensional nonnegative matrix. Its spectral radius yields an explicit sufficient discount threshold, and a corresponding equivalent weighted product norm is constructed to establish the contraction property. Moreover, for an infinite-horizon control problem with convex control constraints and an accumulated discounted running cost, we derive a Pontryagin-type stochastic maximum principle, its equivalent pointwise normal-cone formulation, and a verification theorem. Finally, a recursive risk-adjusted portfolio example is given to demonstrate the applications of our theoretical results, and a projection-type sufficient optimality condition for this example is derived.
