{"title":"Fitted Operator Finite Difference Method for Singularly Perturbed Parabolic Convection-Diffusion Type","authors":"T. A. Bullo, G. Duressa","doi":"10.5121/IEIJ.2021.5101","DOIUrl":"https://doi.org/10.5121/IEIJ.2021.5101","url":null,"abstract":"In this paper, we study the numerical solution of singularly perturbed parabolic convection-diffusion type with boundary layers at the right side. To solve this problem, the backward-Euler with Richardson extrapolation method is applied on the time direction and the fitted operator finite difference method on the spatial direction is used, on the uniform grids. The stability and consistency of the method were established very well to guarantee the convergence of the method. Numerical experimentation is carried out on model examples, and the results are presented both in tables and graphs. Further, the present method gives a more accurate solution than some existing methods reported in the literature.","PeriodicalId":183820,"journal":{"name":"DecisionSciRN: Other Decision-Making in Mathematics (Sub-Topic)","volume":"20 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-03-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116628905","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Nonparametric Density Estimation and Bandwidth Selection with B-spline bases: a Novel Galerkin Method","authors":"J. Kirkby, Álvaro Leitao, D. Nguyen","doi":"10.2139/ssrn.3769651","DOIUrl":"https://doi.org/10.2139/ssrn.3769651","url":null,"abstract":"Abstract A general and efficient nonparametric density estimation procedure for local bases, including B-splines, is proposed, which employs a novel statistical Galerkin method combined with basis duality theory. To select the bandwidth, an efficient cross-validation procedure is introduced, based on closed-form expressions in terms of the primal and dual B-spline basis. By utilizing a closed-form expression for the dual basis, the least-squares cross validation formula is calculated in closed-form, enabling an efficient estimation of the optimal bandwidth. The full computational procedure achieves optimal complexity, and is very accurate in comparisons with existing estimation procedures, including state-of-the-art kernel density estimators. The presented theoretical results are supported by extensive numerical experiments, which demonstrate the efficiency and accuracy of the new methodology. This new approach provides a complete and optimally efficient framework for density estimation with a B-spline basis, based on simple and elegant closed-form estimators with theoretical convergence results that are substantiated in numerical experiments.","PeriodicalId":183820,"journal":{"name":"DecisionSciRN: Other Decision-Making in Mathematics (Sub-Topic)","volume":"7 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-01-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114082141","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Constrained Utility Deviation-Risk Optimization and Time-consistent HJB Equation","authors":"Jiawen Gu, Shijing Si, Harry Zheng","doi":"10.2139/ssrn.3384245","DOIUrl":"https://doi.org/10.2139/ssrn.3384245","url":null,"abstract":"In this paper we propose a unified utility deviation-risk model which covers both utility maximization and mean-variance analysis as special cases. We derive the time-consistent Hamilton-Jacobi-Bellman (HJB) equation for the equilibrium value function and significantly reduce the number of state variables, which makes the HJB equation derived in this paper much easier to solve than the extended HJB equation in the literature. We illustrate the usefulness of the time-consistent HJB equation with several examples which recover the known results in the literature and go beyond, including a mean-variance model with stochastic volatility dependent risk aversion, a utility deviation-risk model with state dependent risk aversion and control constraint, and a constrained portfolio selection model. The numerical and statistical tests show that the utility and deviation-risk have a significant impact on the equilibrium control strategy and the distribution of the terminal wealth.","PeriodicalId":183820,"journal":{"name":"DecisionSciRN: Other Decision-Making in Mathematics (Sub-Topic)","volume":"78 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134271291","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Complex, Dynamic and Contingent Social Processes as Patterns of Decision-Making Events – Philosophical and Mathematical Foundations","authors":"Bruno da Rocha Braga","doi":"10.2139/ssrn.3147371","DOIUrl":"https://doi.org/10.2139/ssrn.3147371","url":null,"abstract":"This work discusses the mathematical foundations of a post-positivist research framework to explain surprising facts in the expected behaviour of any complex, dynamic and contingent phenomenon, reconciling the ontological and epistemological assumptions of Critical Realism with the American Pragmatism. Theoretical propositions turned into a set of grammar rules can acknowledge a pattern of sequences of decision-making events on conducting individual actions or social interactions with partners. The result is a discrete mathematical model for a category of social process that needs modifications to explain all instances of the surprising fact as a new event outcome regarding specific configurations of other past event outcomes that become the historical context for its generation. The data-grounded theory refinement is possible through structural comparison between cases belonging to the same category of social process, but differing in respect to this contingent pattern of sequences of events. As an example, the case study of the competence development process in the firm is detailed in terms of a grammar of its socioeconomic bevahior to support the generation of middle-range theories of the firm.","PeriodicalId":183820,"journal":{"name":"DecisionSciRN: Other Decision-Making in Mathematics (Sub-Topic)","volume":"37 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-05-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134132372","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}