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On the Expected Discounted Penalty Function Using Physics-Informed Neural Network 利用物理信息神经网络研究预期贴现惩罚函数
IF 1.4 4区 数学 Q1 MATHEMATICS Pub Date : 2023-12-28 DOI: 10.1155/2023/9950023
Jiayu Wang, Houchun Wang
We study the expected discounted penalty at ruin under a stochastic discount rate for the compound Poisson risk model with a threshold dividend strategy. The discount rate is modeled by a Poisson process and a standard Brownian motion. By applying the differentiation method and total expectation formula, we obtain an integrodifferential equation for the expected discounted penalty function. From this integrodifferential equation, a renewal equation and an asymptotic formula satisfied by the expected discounted penalty function are derived. In order to solve the integrodifferential equation, we use a physics-informed neural network (PINN) for the first time in risk theory and obtain the numerical solutions of the expected discounted penalty function in some special cases of the penalty at ruin.
我们研究了具有门槛股息策略的复合泊松风险模型在随机贴现率条件下毁灭时的预期贴现惩罚。贴现率的模型是泊松过程和标准布朗运动。通过运用微分法和总期望公式,我们得到了期望贴现惩罚函数的积分微分方程。根据这个积分微分方程,可以得出预期贴现惩罚函数所满足的更新方程和渐近公式。为了求解这个整微分方程,我们在风险理论中首次使用了物理信息神经网络(PINN),并得到了预期贴现惩罚函数在一些毁灭惩罚特殊情况下的数值解。
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引用次数: 0
Well-Posedness in Variable-Exponent Function Spaces for the Three-Dimensional Micropolar Fluid Equations 三维微波流体方程在变指数函数空间中的好求解性
IF 1.4 4区 数学 Q1 MATHEMATICS Pub Date : 2023-12-26 DOI: 10.1155/2023/4083997
Muhammad Zainul Abidin, Muhammad Marwan, Naeem Ullah, Ahmed Mohamed Zidan
In this paper, we work on the Cauchy problem of the three-dimensional micropolar fluid equations. For small initial data, in the variable-exponent Fourier–Besov spaces, we achieve the global well-posedness result. The Littlewood–Paley decomposition method and the Fourier-localization technique are main tools to obtain the results. Moreover, the results discussed in our work show the Gevrey class regularity of solution to the Cauchy problem of micropolar fluid equations.
本文研究了三维微波流体方程的 Cauchy 问题。对于较小的初始数据,在变分量傅里叶-贝索夫空间中,我们得到了全局好求结果。Littlewood-Paley 分解法和傅里叶定位技术是获得结果的主要工具。此外,我们工作中讨论的结果显示了微极性流体方程 Cauchy 问题解的 Gevrey 类正则性。
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引用次数: 0
Application of Asymptotic Analysis of a High-Dimensional HJB Equation to Portfolio Optimization 高维 HJB 方程渐近分析在投资组合优化中的应用
IF 1.4 4区 数学 Q1 MATHEMATICS Pub Date : 2023-12-21 DOI: 10.1155/2023/3399493
Lei Hu
In this paper, we consider a portfolio optimization problem where the wealth consists of investing into a risky asset with a slow mean-reverting volatility and receiving an uncontrollable stochastic cash flow under the exponential utility. The Hamilton–Jacobi–Bellman equation formulated from the optimal investment problem is a high-dimensional nonlinear partial differential equation and difficult to find its analytical or numerical solutions. The paper provides a tractable asymptotic approach which treats the initial problem as a perturbation around the constant volatility problem. In this paper, we present a formal derivation of asymptotic approximation and prove the accuracy of the value function. Moreover, an illustrative example is provided to assess our approximate strategy and value function.
在本文中,我们考虑了一个投资组合优化问题,其财富包括投资于具有缓慢均值回复波动性的风险资产,并获得指数效用下的不可控随机现金流。由最优投资问题推导出的 Hamilton-Jacobi-Bellman 方程是一个高维非线性偏微分方程,很难找到其分析或数值解。本文提供了一种可操作的渐近方法,将初始问题视为恒定波动问题周围的扰动。本文提出了渐近逼近法的正式推导,并证明了值函数的准确性。此外,我们还提供了一个示例来评估我们的近似策略和价值函数。
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引用次数: 0
Retracted: Research on the Spread Path and Evolution Causes of Oral Language in the Digital Era 撤回:数字时代口语的传播路径和演变原因研究
IF 1.4 4区 数学 Q1 MATHEMATICS Pub Date : 2023-12-20 DOI: 10.1155/2023/9878209
Journal of Mathematics
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引用次数: 0
Retracted: Classification and Analysis of College Students’ Skills Using Hybrid AI Models 撤回:利用混合人工智能模型对大学生的技能进行分类和分析
IF 1.4 4区 数学 Q1 MATHEMATICS Pub Date : 2023-12-20 DOI: 10.1155/2023/9842979
Journal of Mathematics
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引用次数: 0
Retracted: Optimization Algorithm of Logistics Transportation Cost of Prefabricated Building Components for Project Management 撤回:面向项目管理的预制建筑构件物流运输成本优化算法
IF 1.4 4区 数学 Q1 MATHEMATICS Pub Date : 2023-12-20 DOI: 10.1155/2023/9858351
Journal of Mathematics
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引用次数: 0
Retracted: Design of Enterprise Economic Information Management System Based on Big Data Integration Algorithm 撤回:基于大数据整合算法的企业经济信息管理系统设计
IF 1.4 4区 数学 Q1 MATHEMATICS Pub Date : 2023-12-20 DOI: 10.1155/2023/9876921
Journal of Mathematics
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引用次数: 0
Retracted: Text Knowledge Acquisition Method of Collaborative Product Design Based on Genetic Algorithm 撤回:基于遗传算法的产品协同设计文本知识获取方法
IF 1.4 4区 数学 Q1 MATHEMATICS Pub Date : 2023-12-20 DOI: 10.1155/2023/9894560
Journal of Mathematics
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引用次数: 0
Retracted: Evaluation Algorithm of Labor Legal Effectiveness for Affirmative Action against Gender Discrimination 撤回:反性别歧视平权行动的劳动法律效力评估算法
IF 1.4 4区 数学 Q1 MATHEMATICS Pub Date : 2023-12-20 DOI: 10.1155/2023/9892024
Journal of Mathematics
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引用次数: 0
Retracted: Data Mining and Analysis of the Compatibility Law of Traditional Chinese Medicines Based on FP-Growth Algorithm 撤回:基于FP-Growth算法的中药相克规律数据挖掘与分析
IF 1.4 4区 数学 Q1 MATHEMATICS Pub Date : 2023-12-20 DOI: 10.1155/2023/9761056
Journal of Mathematics
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引用次数: 0
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Journal of Mathematics
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