Pub Date : 2024-07-18DOI: 10.1007/s40314-024-02844-x
Jianyu Huo, Qing Zhou
We investigate the optimal decisions on investment, consumption and purchasing life insurance of a household with two consecutive generations, say parents and children. Parents can invest in risk-free and risky assets, with the risky asset’s price driven by the Heston local-stochastic volatility model, better reflecting market conditions. Life insurance can be purchased to hedge against wealth loss from parents’ unexpected death before retirement, especially if children have no income. Meanwhile, utility functions of the parents and children are individually considered in relation to the uncertain lifetime. The objective of the household is to appropriately maximize the weighted average of the respective utilities of parents and children. In order to derive the optimal strategies, we adopt a dual method, Legendre transformation, and an asymptotic expansion technique to solve the associated Hamilton–Jacobi–Bellman equation achieved by a dynamic programming approach. Finally, an asymptotic solution is obtained and numerical examples are provided to illustrate the impacts of some important parameters on the optimal strategies.
{"title":"Legendre transform dual-asymptotic solution for optimal investment, consumption and life insurance strategy under the HLSV model","authors":"Jianyu Huo, Qing Zhou","doi":"10.1007/s40314-024-02844-x","DOIUrl":"https://doi.org/10.1007/s40314-024-02844-x","url":null,"abstract":"<p>We investigate the optimal decisions on investment, consumption and purchasing life insurance of a household with two consecutive generations, say parents and children. Parents can invest in risk-free and risky assets, with the risky asset’s price driven by the Heston local-stochastic volatility model, better reflecting market conditions. Life insurance can be purchased to hedge against wealth loss from parents’ unexpected death before retirement, especially if children have no income. Meanwhile, utility functions of the parents and children are individually considered in relation to the uncertain lifetime. The objective of the household is to appropriately maximize the weighted average of the respective utilities of parents and children. In order to derive the optimal strategies, we adopt a dual method, Legendre transformation, and an asymptotic expansion technique to solve the associated Hamilton–Jacobi–Bellman equation achieved by a dynamic programming approach. Finally, an asymptotic solution is obtained and numerical examples are provided to illustrate the impacts of some important parameters on the optimal strategies.</p>","PeriodicalId":51278,"journal":{"name":"Computational and Applied Mathematics","volume":"61 1","pages":""},"PeriodicalIF":2.6,"publicationDate":"2024-07-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141737801","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-07-16DOI: 10.1007/s40314-024-02841-0
Jun Ji
{"title":"Alternative algebraic perturbation expressions for the core-EP inverse of a matrix","authors":"Jun Ji","doi":"10.1007/s40314-024-02841-0","DOIUrl":"https://doi.org/10.1007/s40314-024-02841-0","url":null,"abstract":"","PeriodicalId":51278,"journal":{"name":"Computational and Applied Mathematics","volume":"5 4","pages":""},"PeriodicalIF":2.6,"publicationDate":"2024-07-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141641077","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-07-15DOI: 10.1007/s40314-024-02638-1
Minghui Xu, Chenhui Zhu, Wei Li, Bin Yang
{"title":"Migrativity of extended binary operations on fuzzy truth values","authors":"Minghui Xu, Chenhui Zhu, Wei Li, Bin Yang","doi":"10.1007/s40314-024-02638-1","DOIUrl":"https://doi.org/10.1007/s40314-024-02638-1","url":null,"abstract":"","PeriodicalId":51278,"journal":{"name":"Computational and Applied Mathematics","volume":"44 7","pages":""},"PeriodicalIF":2.6,"publicationDate":"2024-07-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141644967","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-07-15DOI: 10.1007/s40314-024-02850-z
Tanmoy Som, Jayanta Sarkar, Dhananjay Gopal
{"title":"Approximating fixed point results for pseudo-contractive map and some remarks on demi-contractive map in the Banach space","authors":"Tanmoy Som, Jayanta Sarkar, Dhananjay Gopal","doi":"10.1007/s40314-024-02850-z","DOIUrl":"https://doi.org/10.1007/s40314-024-02850-z","url":null,"abstract":"","PeriodicalId":51278,"journal":{"name":"Computational and Applied Mathematics","volume":"28 5","pages":""},"PeriodicalIF":2.6,"publicationDate":"2024-07-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141645356","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-07-15DOI: 10.1007/s40314-024-02852-x
Vinícius Francisco Wasques
{"title":"A numerical approach to fuzzy partial differential equations with interactive fuzzy values: application to the heat equation","authors":"Vinícius Francisco Wasques","doi":"10.1007/s40314-024-02852-x","DOIUrl":"https://doi.org/10.1007/s40314-024-02852-x","url":null,"abstract":"","PeriodicalId":51278,"journal":{"name":"Computational and Applied Mathematics","volume":"32 4","pages":""},"PeriodicalIF":2.6,"publicationDate":"2024-07-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141646785","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-07-15DOI: 10.1007/s40314-024-02781-9
R. Hussain, Zahid Hussain
{"title":"Belief and plausible divergence measures: a novel approach to multicriteria decision making with modified CODAS","authors":"R. Hussain, Zahid Hussain","doi":"10.1007/s40314-024-02781-9","DOIUrl":"https://doi.org/10.1007/s40314-024-02781-9","url":null,"abstract":"","PeriodicalId":51278,"journal":{"name":"Computational and Applied Mathematics","volume":"31 3","pages":""},"PeriodicalIF":2.6,"publicationDate":"2024-07-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141647610","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-07-13DOI: 10.1007/s40314-024-02829-w
Oluwatosin Temitope Mewomo, Victor Amarachi Uzor, Aviv Gibali
In this paper, we focus on some split inverse problems, namely the split equality variational inequalities and common fixed point problems, and combine various operator theory techniques to establish minimum-norm strong convergence for our proposed method. We present two strong convergent results with (and without) reference to the monotonicity property of the cost operators. Our convergence analyses assume very mild conditions and thus generalize and extend recent related results in the literature. Furthermore, several numerical examples illustrate the practical potentials and advantages of our proposed algorithm.
{"title":"A strongly convergent algorithm for solving split equality problems beyond monotonicity","authors":"Oluwatosin Temitope Mewomo, Victor Amarachi Uzor, Aviv Gibali","doi":"10.1007/s40314-024-02829-w","DOIUrl":"https://doi.org/10.1007/s40314-024-02829-w","url":null,"abstract":"<p>In this paper, we focus on some split inverse problems, namely the split equality variational inequalities and common fixed point problems, and combine various operator theory techniques to establish minimum-norm strong convergence for our proposed method. We present two strong convergent results with (and without) reference to the monotonicity property of the cost operators. Our convergence analyses assume very mild conditions and thus generalize and extend recent related results in the literature. Furthermore, several numerical examples illustrate the practical potentials and advantages of our proposed algorithm.</p>","PeriodicalId":51278,"journal":{"name":"Computational and Applied Mathematics","volume":"55 1","pages":""},"PeriodicalIF":2.6,"publicationDate":"2024-07-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141610923","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-07-13DOI: 10.1007/s40314-024-02842-z
Yuan Bao, Sibo Yang, Zhaoliang Meng, Chaobin Liu, Zhongxuan Luo
In this paper, we construct a new mixed finite element for the Stokes problem on general convex quadrilateral partitions. The velocity is approximated by piecewise polynomial element space, and the pressure is approximated by piecewise constant. Moreover, we assert that the discrete velocity is second-order convergent in discrete (H^{1}) seminorm, and the convergence order of the pressure solution can be improved to second by a post-processing for Stokes problems. Lastly, numerical tests verify the convergence analysis.
{"title":"A second-order convergent nonconforming polynomial stokes element on quadrilateral meshes","authors":"Yuan Bao, Sibo Yang, Zhaoliang Meng, Chaobin Liu, Zhongxuan Luo","doi":"10.1007/s40314-024-02842-z","DOIUrl":"https://doi.org/10.1007/s40314-024-02842-z","url":null,"abstract":"<p>In this paper, we construct a new mixed finite element for the Stokes problem on general convex quadrilateral partitions. The velocity is approximated by piecewise polynomial element space, and the pressure is approximated by piecewise constant. Moreover, we assert that the discrete velocity is second-order convergent in discrete <span>(H^{1})</span> seminorm, and the convergence order of the pressure solution can be improved to second by a post-processing for Stokes problems. Lastly, numerical tests verify the convergence analysis.</p>","PeriodicalId":51278,"journal":{"name":"Computational and Applied Mathematics","volume":"7 1","pages":""},"PeriodicalIF":2.6,"publicationDate":"2024-07-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141610924","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-07-12DOI: 10.1007/s40314-024-02813-4
Hadi Mohammadi-Firouzjaei, Hojatollah Adibi, Mehdi Dehghan
The aim of this paper is to implement the high-order local discontinuous Galerkin method (LDGM) for solving partial integro-differential equations (PIDEs) in two dimensions. Time marching method and the transform-based method known as the non-time marching method can be used to discretize temporal terms. The combination of a small time step size in time marching methods and a high-order scheme in space with many degrees of freedom requires a considerable amount of computational time. In order to address this limitation, we propose an algorithm based on a combination of the Laplace transform and LDGM for solving fourth-order time-fractional (TF) PIDEs with weakly singular kernels. Unlike time-marching approaches, the transform-based method has a much lower computational complexity and can take advantage of parallel computing. A numerical experiment validates the accuracy and applicability of the proposed temporal discretization approach and also shows that k-degree LDG solutions have a (k + 1) convergence rate.
{"title":"Computational study based on the Laplace transform and local discontinuous Galerkin methods for solving fourth-order time-fractional partial integro-differential equations with weakly singular kernels","authors":"Hadi Mohammadi-Firouzjaei, Hojatollah Adibi, Mehdi Dehghan","doi":"10.1007/s40314-024-02813-4","DOIUrl":"https://doi.org/10.1007/s40314-024-02813-4","url":null,"abstract":"<p>The aim of this paper is to implement the high-order local discontinuous Galerkin method (LDGM) for solving partial integro-differential equations (PIDEs) in two dimensions. Time marching method and the transform-based method known as the non-time marching method can be used to discretize temporal terms. The combination of a small time step size in time marching methods and a high-order scheme in space with many degrees of freedom requires a considerable amount of computational time. In order to address this limitation, we propose an algorithm based on a combination of the Laplace transform and LDGM for solving fourth-order time-fractional (TF) PIDEs with weakly singular kernels. Unlike time-marching approaches, the transform-based method has a much lower computational complexity and can take advantage of parallel computing. A numerical experiment validates the accuracy and applicability of the proposed temporal discretization approach and also shows that <i>k</i>-degree LDG solutions have a <span>(k + 1)</span> convergence rate.</p>","PeriodicalId":51278,"journal":{"name":"Computational and Applied Mathematics","volume":"34 1","pages":""},"PeriodicalIF":2.6,"publicationDate":"2024-07-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141610848","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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