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Optimal Timing of Business Conversion for Solvency Improvement 改善偿付能力的最佳业务转型时机
IF 0.8 4区 数学
Acta Mathematicae Applicatae Sinica, English Series Pub Date : 2024-06-05 DOI: 10.1007/s10255-024-1048-0
Peng Li, Ming Zhou
{"title":"Optimal Timing of Business Conversion for Solvency Improvement","authors":"Peng Li, Ming Zhou","doi":"10.1007/s10255-024-1048-0","DOIUrl":"https://doi.org/10.1007/s10255-024-1048-0","url":null,"abstract":"<p>In this paper, we study the optimal timing to convert the risk of business for an insurance company in order to improve its solvency. The cash flow of company evolves according to a jump-diffusion process. Business conversion option offers the company an opportunity to transfer the jump risk business out. In exchange for this option, the company needs to pay both fixed and proportional transaction costs. The proportional cost can also be seen as the profit loading of the jump risk business. We formulated this problem as an optimal stopping problem. By solving this stopping problem, we find that the optimal timing of business conversion mainly depends on the profit loading of the jump risk business. A larger profit loading would make the conversion option valueless. The fixed cost, however, only delays the optimal timing of business conversion. In the end, numerical results are provided to illustrate the impacts of transaction costs and environmental parameters to the optimal strategies.</p>","PeriodicalId":6951,"journal":{"name":"Acta Mathematicae Applicatae Sinica, English Series","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2024-06-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141256103","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
Strong Limit Theorems for Weighted Sums under the Sub-linear Expectations 次线性期望下加权和的强极限定理
IF 0.8 4区 数学
Acta Mathematicae Applicatae Sinica, English Series Pub Date : 2024-06-05 DOI: 10.1007/s10255-024-1127-2
Feng-xiang Feng, Ding-cheng Wang, Qun-ying Wu, Hai-wu Huang
{"title":"Strong Limit Theorems for Weighted Sums under the Sub-linear Expectations","authors":"Feng-xiang Feng, Ding-cheng Wang, Qun-ying Wu, Hai-wu Huang","doi":"10.1007/s10255-024-1127-2","DOIUrl":"https://doi.org/10.1007/s10255-024-1127-2","url":null,"abstract":"<p>In this article, we study strong limit theorems for weighted sums of extended negatively dependent random variables under the sub-linear expectations. We establish general strong law and complete convergence theorems for weighted sums of extended negatively dependent random variables under the sub-linear expectations. Our results of strong limit theorems are more general than some related results previously obtained by Thrum (1987), Li et al. (1995) and Wu (2010) in classical probability space.</p>","PeriodicalId":6951,"journal":{"name":"Acta Mathematicae Applicatae Sinica, English Series","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2024-06-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141256192","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
Sliced Average Variance Estimation for Tensor Data 张量数据的切分平均方差估计
IF 0.8 4区 数学
Acta Mathematicae Applicatae Sinica, English Series Pub Date : 2024-06-05 DOI: 10.1007/s10255-024-1024-8
Chuan-quan Li, Pei-wen Xiao, Chao Ying, Xiao-hui Liu
{"title":"Sliced Average Variance Estimation for Tensor Data","authors":"Chuan-quan Li, Pei-wen Xiao, Chao Ying, Xiao-hui Liu","doi":"10.1007/s10255-024-1024-8","DOIUrl":"https://doi.org/10.1007/s10255-024-1024-8","url":null,"abstract":"<p>Tensor data have been widely used in many fields, e.g., modern biomedical imaging, chemometrics, and economics, but often suffer from some common issues as in high dimensional statistics. How to find their low-dimensional latent structure has been of great interest for statisticians. To this end, we develop two efficient tensor sufficient dimension reduction methods based on the sliced average variance estimation (SAVE) to estimate the corresponding dimension reduction subspaces. The first one, entitled tensor sliced average variance estimation (TSAVE), works well when the response is discrete or takes finite values, but is not <span>(sqrt n)</span> consistent for continuous response; the second one, named bias-correction tensor sliced average variance estimation (CTSAVE), is a de-biased version of the TSAVE method. The asymptotic properties of both methods are derived under mild conditions. Simulations and real data examples are also provided to show the superiority of the efficiency of the developed methods.</p>","PeriodicalId":6951,"journal":{"name":"Acta Mathematicae Applicatae Sinica, English Series","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2024-06-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141256217","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
Multiple Normalized Solutions for Nonlinear Biharmonic Schrödinger Equations in ℝN with L2-Subcritical Growth 具有 L2 次临界增长的ℝN 中非线性双谐波薛定谔方程的多重归一化解决方案
IF 0.8 4区 数学
Acta Mathematicae Applicatae Sinica, English Series Pub Date : 2024-06-01 DOI: 10.1007/s10255-024-1131-6
Jun Wang, Li Wang, Ji-xiu Wang
{"title":"Multiple Normalized Solutions for Nonlinear Biharmonic Schrödinger Equations in ℝN with L2-Subcritical Growth","authors":"Jun Wang, Li Wang, Ji-xiu Wang","doi":"10.1007/s10255-024-1131-6","DOIUrl":"https://doi.org/10.1007/s10255-024-1131-6","url":null,"abstract":"<p>In this article, we consider the existence of normalized solutions for the following nonlinear biharmonic Schrödinger equations</p><span>$$left{{matrix{{{Delta ^2}u = lambda u + hleft({varepsilon x} right),fleft(u right),} &amp; {x in mathbb{R}{^N},} cr {int_{mathbb{R}{^N}} {{{left| u right|}^2}dx = {c^2},}} &amp; {x in mathbb{R}{^N},} cr}} right.$$</span><p>where <i>c, ε</i> &gt; 0; <i>N</i> ≥ 5; <i>λ</i> ∈ ℝ is a Lagrange multiplier and is unknown, <i>h</i> ∈ <i>C</i>(ℝ<sup><i>N</i></sup>; [0;∞)); <i>f</i>: ℝ → ℝ is continuous function satisfying <i>L</i><sup>2</sup>-subcritical growth. When <i>ε</i> is small enough, we get multiple normalized solutions. Moreover, we also obtain orbital stability of the solutions.</p>","PeriodicalId":6951,"journal":{"name":"Acta Mathematicae Applicatae Sinica, English Series","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2024-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141192338","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
Sharp Interface Limit for the One-dimensional Compressible Navier-Stokes/Allen-Cahn System with Composite Waves 具有复合波的一维可压缩纳维-斯托克斯/阿伦-卡恩系统的锐界面极限
IF 0.8 4区 数学
Acta Mathematicae Applicatae Sinica, English Series Pub Date : 2024-06-01 DOI: 10.1007/s10255-024-1130-7
Ya-zhou Chen, Yi Peng, Xiao-ding Shi
{"title":"Sharp Interface Limit for the One-dimensional Compressible Navier-Stokes/Allen-Cahn System with Composite Waves","authors":"Ya-zhou Chen, Yi Peng, Xiao-ding Shi","doi":"10.1007/s10255-024-1130-7","DOIUrl":"https://doi.org/10.1007/s10255-024-1130-7","url":null,"abstract":"<p>This paper is concerned with the sharp interface limit of Cauchy problem for the one-dimensional compressible Navier-Stokes/Allen-Cahn system with a composite wave consisting of the superposition of a rarefaction wave and a shock wave. Under the assumption that the viscosity coefficient and the reciprocal of mobility coefficient are directly proportional to the interface thickness, we first convert the sharp interface limit of the system into the large time behavior of the composite wave via a natural scaling. Then we prove that the composite wave is asymptotically stable under the small initial perturbations and the small strength of the rarefaction and shock wave. Finally, we show the solution of the Cauchy problem exists for all time, and converges to the composite wave solution of the corresponding Euler equations as the thickness of the interface tends to zero. The proof is mainly based on the energy method and the relative entropy.</p>","PeriodicalId":6951,"journal":{"name":"Acta Mathematicae Applicatae Sinica, English Series","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2024-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141198275","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
Fourier Transform of Anisotropic Hardy Spaces Associated with Ball Quasi-Banach Function Spaces and Its Applications to Hardy-Littlewood Inequalities 与球准巴纳赫函数空间相关的各向异性哈代空间的傅立叶变换及其在哈代-利特尔伍德不等式中的应用
IF 0.8 4区 数学
Acta Mathematicae Applicatae Sinica, English Series Pub Date : 2024-06-01 DOI: 10.1007/s10255-024-1124-5
Chao-an Li, Xian-jie Yan, Da-chun Yang
{"title":"Fourier Transform of Anisotropic Hardy Spaces Associated with Ball Quasi-Banach Function Spaces and Its Applications to Hardy-Littlewood Inequalities","authors":"Chao-an Li, Xian-jie Yan, Da-chun Yang","doi":"10.1007/s10255-024-1124-5","DOIUrl":"https://doi.org/10.1007/s10255-024-1124-5","url":null,"abstract":"<p>Let <i>A</i> be a general expansive matrix and <i>X</i> be a ball quasi-Banach function space on ℝ<sup><i>n</i></sup>, whose certain power (namely its convexification) supports a Fefferman-Stein vector-valued maximal inequality and the associate space of whose other power supports the boundedness of the powered Hardy-Littlewood maximal operator. Let <i>H</i><span>\u0000<sup><i>A</i></sup><sub><i>X</i></sub>\u0000</span>(ℝ<sup><i>n</i></sup>) be the anisotropic Hardy space associated with <i>A</i> and <i>X</i>. The authors first prove that the Fourier transform of <i>f</i> ∈ <i>H</i><span>\u0000<sup><i>A</i></sup><sub><i>X</i></sub>\u0000</span>(ℝ<sup><i>n</i></sup>) coincides with a continuous function <i>F</i> on ℝ<sup><i>n</i></sup> in the sense of tempered distributions. Moreover, the authors obtain a pointwise inequality that the function <i>F</i> is less than the product of the anisotropic Hardy space norm of <i>f</i> and a step function with respect to the transpose matrix of the expansive matrix <i>A</i>. Applying this, the authors further induce a higher order convergence for the function <i>F</i> at the origin and give a variant of the Hardy-Littlewood inequality in <i>H</i><span>\u0000<sup><i>A</i></sup><sub><i>X</i></sub>\u0000</span>(ℝ<sup><i>n</i></sup>). All these results have a wide range of applications. Particularly, the authors apply these results, respectively, to classical (variable and mixed-norm) Lebesgue spaces, Lorentz spaces, Orlicz spaces, Orlicz-slice spaces, and local generalized Herz spaces and, even on the last four function spaces, the obtained results are completely new.</p>","PeriodicalId":6951,"journal":{"name":"Acta Mathematicae Applicatae Sinica, English Series","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2024-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141192395","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
Two-grid Method of Expanded Mixed Finite Element Approximations for Parabolic Integro-differential Optimal Control Problems 抛物线积分微分优化控制问题的双网格扩展混合有限元逼近法
IF 0.8 4区 数学
Acta Mathematicae Applicatae Sinica, English Series Pub Date : 2024-06-01 DOI: 10.1007/s10255-024-1099-2
Yan-ping Chen, Jian-wei Zhou, Tian-liang Hou
{"title":"Two-grid Method of Expanded Mixed Finite Element Approximations for Parabolic Integro-differential Optimal Control Problems","authors":"Yan-ping Chen, Jian-wei Zhou, Tian-liang Hou","doi":"10.1007/s10255-024-1099-2","DOIUrl":"https://doi.org/10.1007/s10255-024-1099-2","url":null,"abstract":"<p>This paper aims to construct a two-grid scheme of fully discretized expanded mixed finite element methods for optimal control problems governed by parabolic integro-differential equations and discuss a priori error estimates. The state variables and co-state variables are discretized by the lowest order Raviart-Thomas mixed finite element, and the control variable is approximated by piecewise constant functions. The time derivative is discretized by the backward Euler method. Firstly, we define some new mixed elliptic projections and prove the corresponding error estimates which play an important role in subsequent convergence analysis. Secondly, we derive a priori error estimates for all variables. Thirdly, we present a two-grid scheme and analyze its convergence. In the two-grid scheme, the solution of the parabolic optimal control problem on a fine grid is reduced to the solution of the parabolic optimal control problem on a much coarser grid and the solution of a decoupled linear algebraic system on the fine grid and the resulting solution still maintains an asymptotically optimal accuracy. At last, a numerical example is presented to verify the theoretical results.</p>","PeriodicalId":6951,"journal":{"name":"Acta Mathematicae Applicatae Sinica, English Series","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2024-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141192339","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
Uniform Large Deviations for Stochastic Generalized Burgers-Huxley Equation Driven by Multiplicative Noise 乘法噪声驱动的随机广义伯格斯-赫胥黎方程的均匀大偏差
IF 0.8 4区 数学
Acta Mathematicae Applicatae Sinica, English Series Pub Date : 2024-06-01 DOI: 10.1007/s10255-024-1129-0
Hui Guo, Xi-liang Li, Jin Ma
{"title":"Uniform Large Deviations for Stochastic Generalized Burgers-Huxley Equation Driven by Multiplicative Noise","authors":"Hui Guo, Xi-liang Li, Jin Ma","doi":"10.1007/s10255-024-1129-0","DOIUrl":"https://doi.org/10.1007/s10255-024-1129-0","url":null,"abstract":"<p>In this paper, we establish a Freidlin-Wentzell type large deviation principle uniformly with respect to initial condition in bounded subsets, that do not necessarily belongs to compact sets, of an infinite dimensional Banach space for stochastic 1D generalized Burgers-Huxley equation driven by multiplicative small noise. The proof is based on the weak convergence approach obtained by [Budhiraja, Dupuis and Salins; Trans. Amer. Math. Soc., 2019].</p>","PeriodicalId":6951,"journal":{"name":"Acta Mathematicae Applicatae Sinica, English Series","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2024-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141192341","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
The P5-saturation Game 五常饱和游戏
IF 0.8 4区 数学
Acta Mathematicae Applicatae Sinica, English Series Pub Date : 2024-06-01 DOI: 10.1007/s10255-024-1125-4
Zhen He, Mei Lu
{"title":"The P5-saturation Game","authors":"Zhen He, Mei Lu","doi":"10.1007/s10255-024-1125-4","DOIUrl":"https://doi.org/10.1007/s10255-024-1125-4","url":null,"abstract":"<p>Let <i>F, G</i> and <i>H</i> be three graphs with <i>G</i> ⊆ <i>H</i>. We call <i>G</i> an <i>F</i>-saturated graph relative to <i>H</i>, if there is no copy of <i>F</i> in <i>G</i> but there is a copy of <i>F</i> in <i>G</i> + <i>e</i> for any <i>e</i> ∈ <i>E</i>(<i>H</i>) <i>E</i>(<i>G</i>). The <i>F</i>-saturation game on host graph <i>H</i> consists of two players, named Max and Min, who alternately add edges of <i>H</i> to <i>G</i> such that each chosen edge avoids creating a copy of <i>F</i> in <i>G</i>, and the players continue to choose edges until <i>G</i> becomes <i>F</i>-saturated relative to <i>H</i>. Max wishes to maximize the length of the game, while Min wishes to minimize the process. Let sat<sub><i>g</i></sub>(<i>F, H</i>) (resp. sat′<sub><i>g</i></sub>(<i>F, H</i>)) denote the number of edges chosen when Max (resp. when Min) starts the game and both players play optimally. In this article, we show that sat<sub><i>g</i></sub>(<i>P</i><sub>5</sub>, <i>K</i><sub><i>n</i></sub>) = sat′<sub><i>g</i></sub>(<i>P</i><sub>5</sub>, <i>K</i><sub><i>n</i></sub>) = <i>n</i> + 2 for <i>n</i> ≥ 15, and sat<sub><i>g</i></sub>(<i>P</i><sub>5</sub>, <i>K</i><sub><i>m,n</i></sub>), sat′<sub><i>g</i></sub>(<i>P</i><sub>5</sub>, <i>K</i><sub><i>m,n</i></sub>) lie in <span>(left{ {m + n - leftlfloor {{{m - 2} over 4}} rightrfloor ,,m + n - leftlceil {{{m - 3} over 4}} rightrceil } right})</span> if <span>(n ge {5 over 2}m)</span> and <i>m</i> ≥ 4, respectively.</p>","PeriodicalId":6951,"journal":{"name":"Acta Mathematicae Applicatae Sinica, English Series","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2024-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141192428","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
Asymptotic Property of Parabolic Equations Involving Pseudo-relativistic Schrödinger Operators 涉及伪相对论薛定谔算子的抛物方程的渐近特性
IF 0.8 4区 数学
Acta Mathematicae Applicatae Sinica, English Series Pub Date : 2024-06-01 DOI: 10.1007/s10255-024-1097-4
Chen Qiao, Su-fang Tang
{"title":"Asymptotic Property of Parabolic Equations Involving Pseudo-relativistic Schrödinger Operators","authors":"Chen Qiao, Su-fang Tang","doi":"10.1007/s10255-024-1097-4","DOIUrl":"https://doi.org/10.1007/s10255-024-1097-4","url":null,"abstract":"<p>In this paper, we investigate parabolic equations involving nonlocal pseudo-relativistic Schrödinger operators (−Δ + <i>m</i><sup>2</sup>)<sup><i>s</i></sup> with <i>s</i> ∈ (0, 1) and mass <i>m</i> &gt; 0 in bounded regions. We establish the asymptotic narrow region principle and asymptotic strong maximum principle for anti symmetric function. As applications, employing the method of moving planes, we show the asymptotical radial symmetry and monotonicity of positive solutions in an unit ball.</p>","PeriodicalId":6951,"journal":{"name":"Acta Mathematicae Applicatae Sinica, English Series","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2024-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141192431","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
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