Mathematical Control and Related Fields最新文献_第7页

Optimal dividend and capital injection strategies in common shock dependence model with time-inconsistent preferences 具有时间不一致偏好的冲击依赖模型中的最优股利和资本注入策略

IF 1.2 4区数学

Mathematical Control and Related Fields Pub Date : 2022-01-01 DOI: 10.3934/mcrf.2022034

Bo Yang, Rongming Wang, Gong Cheng

{"title":"Optimal dividend and capital injection strategies in common shock dependence model with time-inconsistent preferences","authors":"Bo Yang, Rongming Wang, Gong Cheng","doi":"10.3934/mcrf.2022034","DOIUrl":"https://doi.org/10.3934/mcrf.2022034","url":null,"abstract":"This paper discusses the optimal dividend and capital injection problems when an insurance company has two lines of business with common shock dependence. Suppose that the manager of the company has time-inconsistent preference, which can be described by a quasi-hyperbolic discount function. The value of the company is measured by the expected discounted dividend payments minus the expected discounted costs of capital injection. The goal is to find out the optimal strategies for maximizing the value of the company. By using the stochastic control techniques, we solve the problems in all cases of time-consistent preference manager, naive manager and sophisticated manager, respectively. The closed-form solutions of the value functions are presented. Our results show that the sophisticated manager is inclined to pay out dividends earlier than the naive manager, time-inconsistent preference manager is more likely to pay dividends in advance than time-consistent preference manager. Furthermore, we provide some numerical analysis to reveal the sensitivity of the optimal dividend strategies to the dependence intensity and the cost of capital injection. The results show that, as the cost of capital injection increases, sophisticated manager will give up capital injection first, followed by naive manager. In addition, we also find that: when the cost of capital injection is low, managers think that the value of the company that undertakes two kinds of insurance with high correlation is higher; while, managers have opposite evaluations, when the cost of capital injection is high.","PeriodicalId":48889,"journal":{"name":"Mathematical Control and Related Fields","volume":"68 1","pages":""},"PeriodicalIF":1.2,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81375275","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Dynamical estimation of a noisy input in a system with a Caputo fractional derivative. The case of continuous measurements of a part of phase coordinates 含卡普托分数阶导数系统中噪声输入的动态估计。连续测量部分相位坐标的情况

IF 1.2 4区数学

Mathematical Control and Related Fields Pub Date : 2022-01-01 DOI: 10.3934/mcrf.2022020

P. Surkov

{"title":"Dynamical estimation of a noisy input in a system with a Caputo fractional derivative. The case of continuous measurements of a part of phase coordinates","authors":"P. Surkov","doi":"10.3934/mcrf.2022020","DOIUrl":"https://doi.org/10.3934/mcrf.2022020","url":null,"abstract":"The problem of estimating (reconstructing) an unknown input for a system of nonlinear differential equations with the Caputo fractional derivative is considered. Information on the position of the system is available for observations and only a part of system's parameters can be measured. The case of measuring all phase coordinates is also presented. The measurements are continuous and the data obtained in them are noisy. The considered problem is ill-posed and, to solve it, we use the method of dynamic inversion. It is based on regularization methods and constructions of positional control theory. In particular, we use the Tikhonov regularization method also known as the smoothing functional method and the Krasovskii extremal aiming method. The approach to estimating an unknown input implies introducing an auxiliary system (a model) with an appropriate rule of forming a control. The proposed estimation algorithm gives approximations of an unknown input and is stable under informational noises and computational errors. As an example illustrating the elaborated technique, a biological model of human immunodeficiency virus disease is used for simulation. The simulation results demonstrate the importance of the approach to on-line estimating unobservable parameters in real processes.","PeriodicalId":48889,"journal":{"name":"Mathematical Control and Related Fields","volume":"6 1","pages":""},"PeriodicalIF":1.2,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81490518","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Feedback control of isolation and contact for SIQR epidemic model via strict Lyapunov function 基于严格Lyapunov函数的SIQR流行病模型隔离与接触反馈控制

IF 1.2 4区数学

Mathematical Control and Related Fields Pub Date : 2022-01-01 DOI: 10.3934/mcrf.2022043

H. Ito, Michael A. Malisoff, F. Mazenc

{"title":"Feedback control of isolation and contact for SIQR epidemic model via strict Lyapunov function","authors":"H. Ito, Michael A. Malisoff, F. Mazenc","doi":"10.3934/mcrf.2022043","DOIUrl":"https://doi.org/10.3934/mcrf.2022043","url":null,"abstract":"We derive feedback control laws for isolation, contact regulation, and vaccination for infectious diseases, using a strict Lyapunov function. We use an SIQR epidemic model describing transmission, isolation via quarantine, and vaccination for diseases to which immunity is long-lasting. Assuming that mass vaccination is not available to completely eliminate the disease in a time horizon of interest, we provide feedback control laws that drive the disease to an endemic equilibrium. We prove the input-to-state stability (or ISS) robustness property on the entire state space, when the immigration perturbation is viewed as the uncertainty. We use an ISS Lyapunov function to derive the feedback control laws. A key ingredient in our analysis is that all compartment variables are present not only in the Lyapunov function, but also in a negative definite upper bound on its time derivative. We illustrate the efficacy of our method through simulations, and we discuss the usefulness of parameters in the controls. Since the control laws are feedback, their values are updated based on data acquired in real time. We also discuss the degradation caused by the delayed data acquisition occurring in practical implementations, and we derive bounds on the delays under which the ISS property is ensured when delays are present.","PeriodicalId":48889,"journal":{"name":"Mathematical Control and Related Fields","volume":"36 1","pages":""},"PeriodicalIF":1.2,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78067332","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 4

New general decay results for a multi-dimensional Bresse system with viscoelastic boundary conditions 具有粘弹性边界条件的多维Bresse系统的新的一般衰减结果

IF 1.2 4区数学

Mathematical Control and Related Fields Pub Date : 2022-01-01 DOI: 10.3934/mcrf.2022050

B. Feng, A. Soufyane, M. Afilal

引用次数: 0

Strong stationarity for a highly nonsmooth optimization problem with control constraints 具有控制约束的高度非光滑优化问题的强平稳性

IF 1.2 4区数学

Mathematical Control and Related Fields Pub Date : 2022-01-01 DOI: 10.3934/mcrf.2022047

Livia M. Betz

引用次数: 4

Sparse optimal control of a quasilinear elliptic PDE in measure spaces 测度空间中拟线性椭圆偏微分方程的稀疏最优控制

IF 1.2 4区数学

Mathematical Control and Related Fields Pub Date : 2022-01-01 DOI: 10.3934/mcrf.2022049

Fabian Hoppe

引用次数: 0

Cost evaluation of finite dimensional and approximate null-controllability for the one dimensional half-heat equation 一维半热方程有限维和近似零可控性的代价评价

IF 1.2 4区数学

Mathematical Control and Related Fields Pub Date : 2022-01-01 DOI: 10.3934/mcrf.2022054

S. Micu, Constantin Nita

引用次数: 0

On the controllability of the BBM equation 关于BBM方程的可控性

IF 1.2 4区数学

Mathematical Control and Related Fields Pub Date : 2022-01-01 DOI: 10.3934/mcrf.2022002

Melek Jellouli

引用次数: 0

The application of a universal separating vector lemma to optimal sampled-data control problems with nonsmooth Mayer cost function 通用分离向量引理在非光滑Mayer代价函数的最优采样数据控制问题中的应用

IF 1.2 4区数学

Mathematical Control and Related Fields Pub Date : 2022-01-01 DOI: 10.3934/mcrf.2022039

S. Adly, L. Bourdin, Gaurav Dhar

引用次数: 1

Optimal strategy for Bayesian two-armed bandit problem with an arched reward function 具有弓形奖励函数的贝叶斯双臂强盗问题的最优策略

IF 1.2 4区数学

Mathematical Control and Related Fields Pub Date : 2022-01-01 DOI: 10.3934/mcrf.2022057

Zengjing Chen, Zhaokun Zhang

引用次数: 0