Optimal control of stochastic delay differential equations and applications to path-dependent financial and economic models

面向金融与经济系统辨识的随机结构储备池计算机

Stochastically Structured Reservoir Computers for Financial and Economic System Identification

本文提出基于随机结构储备池计算机的金融经济系统辨识仿真框架，结合保结构嵌入与图引导耦合矩阵，通过约束优化满足相关约束，经实证验证可有效捕捉复杂非线性模式，支撑不确定性下的可解释预测。

A Singular Differential Equation Stemming from an Optimal Control Problem in Financial Economics

We consider the ordinary differential equation $x^2 u'' = axu'+bu-c(u'-1)^2, x\in (0,x_0)$, with $a\in\mathbb{R}, b\in\mathbb{R}$, $c>0$ and the singular initial condition $u(0)=0$, which in financial economics describes optimal disposal of an asset in a market with liquidity effects. It is shown in the paper that if $a+b < 0$ then no solutions exist, whereas if $a+b\ge0$ then there are infinitely many solutions with indistinguishable asymptotics near 0. Moreover, it is proved that in the latter case there is precisely one solution $u$ corresponding to the choice $x_0=\infty$ which is such tha…

带时滞的有限时域G-SDE松弛最优控制问题及其在经济学中的应用

Relaxed Optimal Control Problem for a Finite Horizon G-SDE with Delay and Its Application in Economics

本文研究有限时域下G-布朗运动驱动的随机时滞微分方程的松弛最优控制存在性，关联其HJB方程与解耦G-正倒向随机时滞微分方程，通过仿真得到最优策略与成本，并给出经济学模型应用。

Smooth solutions to discounted reward control problems with unbounded discount rate and financial applications

We consider a discounted reward control problem in continuous time stochastic environment where the discount rate might be an unbounded function of the control process. We provide a set of general assumptions to ensure that there exists a smooth classical solution to the corresponding HJB equation. Moreover, some verification reasoning are provided and the possible extension to dynamic games is discussed. At the end of the paper consumption - investment problems arising in financial economics are considered.

On Positive Solutions of a Delay Equation Arising When Trading in Financial Markets

We consider a discrete-time, linear state equation with delay which arises as a model for a trader's account value when buying and selling a risky asset in a financial market. The state equation includes a nonnegative feedback gain $α$ and a sequence $v(k)$ which models asset returns which are within known bounds but otherwise arbitrary. We introduce two thresholds, $α_-$ and $α_+$, depending on these bounds, and prove that for $α< α_-$, state positivity is guaranteed for all time and all asset-return sequences; i.e., bankruptcy is ruled out and positive solutions of the state equation are con…

随机延迟微分博弈：金融建模与机器学习算法

Stochastic Delay Differential Games: Financial Modeling and Machine Learning Algorithms

本文针对随机延迟微分博弈的高维闭环 Nash 均衡求解问题，提出以独立循环神经网络参数化各参与者控制，并结合改进 Brown 虚拟博弈与深度学习训练，同时在已知金融问题和新建解析基准上验证其有效性。