Pub Date : 2018-02-06DOI: 10.14505/JMEF.V3.2(5).01
Alessia Donato
In this article, we propose an algorithm for the resolution of fourth degree equations, explicitly showing the solution method used, and we compare the results ob- tained with the Matlab “root” command.
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Pub Date : 2017-12-31DOI: 10.14505/JMEF.V3.2(5).03
Aleksandar Vasilev
In this lecture notes, we study filters and limits in a feasible sufficiently general way for many applications to Physics, Economics and Social Science. In particular we analyze: Filters; Filter bases; Basic example in topological spaces; Basic examples in preordered spaces; Filtered spaces; Induced filter bases; Examples in topological spaces; Examples on the real line; Limits; Limits with respect to filter bases; Limits with respect to filter bases on subspaces; Limits and topology; Limits of functions on topological spaces; Limits of functions on a topological subspace; Some basic theorems for topology; Unicity of the limit in Hausdor spaces; Limits and functionals; Limits for real functional; Limits and operations; Local boundness; Complements; Limits and convergence of filtered bases; Limit of composition.
{"title":"Filters and limits in filtered spaces","authors":"Aleksandar Vasilev","doi":"10.14505/JMEF.V3.2(5).03","DOIUrl":"https://doi.org/10.14505/JMEF.V3.2(5).03","url":null,"abstract":"In this lecture notes, we study filters and limits in a feasible sufficiently general way for many applications to Physics, Economics and Social Science. In particular we analyze: \u0000 \u0000Filters; \u0000 \u0000 \u0000Filter bases; \u0000 \u0000 \u0000Basic example in topological spaces; \u0000 \u0000 \u0000Basic examples in preordered spaces; \u0000 \u0000 \u0000Filtered spaces; \u0000 \u0000 \u0000Induced filter bases; \u0000 \u0000 \u0000Examples in topological spaces; \u0000 \u0000 \u0000Examples on the real line; \u0000 \u0000 \u0000Limits; \u0000 \u0000 \u0000Limits with respect to filter bases; \u0000 \u0000 \u0000Limits with respect to filter bases on subspaces; \u0000 \u0000 \u0000Limits and topology; \u0000 \u0000 \u0000Limits of functions on topological spaces; \u0000 \u0000 \u0000Limits of functions on a topological subspace; \u0000 \u0000 \u0000Some basic theorems for topology; \u0000 \u0000 \u0000Unicity of the limit in Hausdor spaces; \u0000 \u0000 \u0000Limits and functionals; \u0000 \u0000 \u0000Limits for real functional; \u0000 \u0000 \u0000Limits and operations; \u0000 \u0000 \u0000Local boundness; \u0000 \u0000 \u0000Complements; \u0000 \u0000 \u0000Limits and convergence of filtered bases; \u0000 \u0000 \u0000Limit of composition. \u0000 \u0000 ","PeriodicalId":367341,"journal":{"name":"Journal of Mathematical Economics and Finance","volume":"88 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2017-12-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131000610","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}
Pub Date : 2017-04-02DOI: 10.14505//JMEF.V2.2(3).04
D. Carfí
We propose, by Schwartz Linear Algebra, a significant development of Laurent Schwartz Distribution Theory. The study is conducted by following the (natu- ral and straightforward) way of Weak Duality among topological vector spaces, aiming at the construction of a feasible, rigorous, quite elementary and manageable frame- work for Quantum Mechanics. It turns out that distribution spaces reveal themselves an environment more capable to help in Quantum Mechanics than previously thought. The goal of the research, introduced here, consists in showing that the most natural state-spaces of a quantum system, in the infinite dimensional case, are indeed dis- tribution spaces. Moreover, we show new, natural and straightforward mathematical structures that reproduce very closely several physical objects and many operational procedures required in Quantum Mechanics, systematizing the algorithms and nota- tions of Dirac Calculus, in such a way that it becomes a more versatile and more powerful tool, than we are used to think of.
{"title":"Motivations and origins of Schwartz Linear Algebra in Quantum Mechanics","authors":"D. Carfí","doi":"10.14505//JMEF.V2.2(3).04","DOIUrl":"https://doi.org/10.14505//JMEF.V2.2(3).04","url":null,"abstract":"We propose, by Schwartz Linear Algebra, a significant development of Laurent Schwartz Distribution Theory. The study is conducted by following the (natu- ral and straightforward) way of Weak Duality among topological vector spaces, aiming at the construction of a feasible, rigorous, quite elementary and manageable frame- work for Quantum Mechanics. It turns out that distribution spaces reveal themselves an environment more capable to help in Quantum Mechanics than previously thought. The goal of the research, introduced here, consists in showing that the most natural state-spaces of a quantum system, in the infinite dimensional case, are indeed dis- tribution spaces. Moreover, we show new, natural and straightforward mathematical structures that reproduce very closely several physical objects and many operational procedures required in Quantum Mechanics, systematizing the algorithms and nota- tions of Dirac Calculus, in such a way that it becomes a more versatile and more powerful tool, than we are used to think of.","PeriodicalId":367341,"journal":{"name":"Journal of Mathematical Economics and Finance","volume":"84 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2017-04-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132604017","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}
Pub Date : 2017-04-02DOI: 10.14505//JMEF.V2.2(3).03
D. Carfí, Alessia Donato
The paper proposes a mathematical model of coopetitive game that ana- lyzes general asymmetric R&D alliances. The coopetitive point of view, which con- siders both collaboration and competition together, allows to analyze the functioning of alliances that arise between small and large firms. Starting from the economic models developed in managerial doctrine and from the model of coopetitive game in- troduced by David Carf`ı, we adopt a mathematical analysis, paying attention to some of the most debated quantitative questions and some analytical topics scarcely covered in the literature: a mathematical model of coopetitive game, particularly suitable for exploring a complex type of asymmetric R&D alliances. We propose a formal coopet- itive approach, with corresponding numerical example, where the coopetitive variable of the model is a real variable. A cooperative effort is suggested even if partners are potentially competitors in the marketplace and they could shape the payoff space by the coopetitive approach. To maximize profits, we suggested: first of all, a complete Pareto analysis (introduced by David Carf`ı), secondly - to share conveniently and fairly the utilities - we propose a Kalai-Smorodinsky solution of the bargaining deci- sion problem, in which the decisional constraint is the Pareto boundary of maximum collective utility.
{"title":"Complete study of a Coopetitive R&D Alliance","authors":"D. Carfí, Alessia Donato","doi":"10.14505//JMEF.V2.2(3).03","DOIUrl":"https://doi.org/10.14505//JMEF.V2.2(3).03","url":null,"abstract":"The paper proposes a mathematical model of coopetitive game that ana- lyzes general asymmetric R&D alliances. The coopetitive point of view, which con- siders both collaboration and competition together, allows to analyze the functioning of alliances that arise between small and large firms. Starting from the economic models developed in managerial doctrine and from the model of coopetitive game in- troduced by David Carf`ı, we adopt a mathematical analysis, paying attention to some of the most debated quantitative questions and some analytical topics scarcely covered in the literature: a mathematical model of coopetitive game, particularly suitable for exploring a complex type of asymmetric R&D alliances. We propose a formal coopet- itive approach, with corresponding numerical example, where the coopetitive variable of the model is a real variable. A cooperative effort is suggested even if partners are potentially competitors in the marketplace and they could shape the payoff space by the coopetitive approach. To maximize profits, we suggested: first of all, a complete Pareto analysis (introduced by David Carf`ı), secondly - to share conveniently and fairly the utilities - we propose a Kalai-Smorodinsky solution of the bargaining deci- sion problem, in which the decisional constraint is the Pareto boundary of maximum collective utility.","PeriodicalId":367341,"journal":{"name":"Journal of Mathematical Economics and Finance","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2017-04-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116975488","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}
Pub Date : 2017-03-31DOI: 10.14505//JMEF.V2.2(3).01
Okura Mahito, Nozaki Hiroyuki
This study discusses two discount systems, namely, the insurance pre- mium discount system, where the policyholder’s valuation is objective, and the book price discount system, where the policyholder’s valuation is subjective. The main pur- pose of this study is to compare these discount systems and show the conditions under which each discount system is chosen by an insurance firm. The main conclusions of this study are as follows. First, the insurance firm chooses the book price discount (insurance premium discount) system if the policyholder’s disutility of loss prevention effort is relatively high (low). Second, the insurance firm chooses the book price discount system when the initial wealth and maximum subjec- tive valuation of the book price discount are large. The insurance firm also chooses the book price discount system when the insurance premium, the amount of damage and effect of the loss prevention effort are small.
{"title":"An Essay on the Subjective Valuation of an Incentive System in an Insurance Market","authors":"Okura Mahito, Nozaki Hiroyuki","doi":"10.14505//JMEF.V2.2(3).01","DOIUrl":"https://doi.org/10.14505//JMEF.V2.2(3).01","url":null,"abstract":"This study discusses two discount systems, namely, the insurance pre- mium discount system, where the policyholder’s valuation is objective, and the book price discount system, where the policyholder’s valuation is subjective. The main pur- pose of this study is to compare these discount systems and show the conditions under which each discount system is chosen by an insurance firm. \u0000The main conclusions of this study are as follows. First, the insurance firm chooses the book price discount (insurance premium discount) system if the policyholder’s disutility of loss prevention effort is relatively high (low). Second, the insurance firm chooses the book price discount system when the initial wealth and maximum subjec- tive valuation of the book price discount are large. The insurance firm also chooses the book price discount system when the insurance premium, the amount of damage and effect of the loss prevention effort are small.","PeriodicalId":367341,"journal":{"name":"Journal of Mathematical Economics and Finance","volume":"33 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2017-03-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116231798","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}
Pub Date : 2016-12-31DOI: 10.14505//JMEF.V2.2(3).02
Aleksandar Vasilev
This paper describes the lottery- and insurance-market equilibrium in an economy with non-convex private- and public-sector employment. In contrast to Vasilev 2017, 2015, the public-sector labor supply decision is a sequential one. This requires two separate insurance market to operate, one for private-sector work, and one for public-sector employment. In addition, given that the labor choice for private- and public-sector hours is made in succession, the insurance market for public emloy- ment needs to open once the other insurance market has closed. This segmentation and sequentiality of insurance markets operation is a new result in the literature and a direct consequence of the double non-convexity, and the sequential nature of the sectoral labor supply decision.
{"title":"Insurance-markets Equilibrium with Sequential Non-convex Private and Public-Sector Labor Supply","authors":"Aleksandar Vasilev","doi":"10.14505//JMEF.V2.2(3).02","DOIUrl":"https://doi.org/10.14505//JMEF.V2.2(3).02","url":null,"abstract":"This paper describes the lottery- and insurance-market equilibrium in an economy with non-convex private- and public-sector employment. In contrast to Vasilev 2017, 2015, the public-sector labor supply decision is a sequential one. This requires two separate insurance market to operate, one for private-sector work, and one for public-sector employment. In addition, given that the labor choice for private- and public-sector hours is made in succession, the insurance market for public emloy- ment needs to open once the other insurance market has closed. This segmentation and sequentiality of insurance markets operation is a new result in the literature and a direct consequence of the double non-convexity, and the sequential nature of the sectoral labor supply decision.","PeriodicalId":367341,"journal":{"name":"Journal of Mathematical Economics and Finance","volume":"41 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2016-12-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125328015","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}
Pub Date : 2016-12-01DOI: 10.14505//JMEF.V2.2(3).05
Daniele Schilirò
In the Theory of Rational Decision Making the psychological aspects are set aside. This contribution seeks to point out the relevance of psychology into eco- nomic decisions. The essay treats the “framing of decisions”, which is a pillar of Kahneman’s behavioral theory. Framing must be considered a special case of the more general phenomenon of dependency from the representation. The best-known risky choice-framing problem, i.e. the “Asian Disease Problem”, is shown where an essen- tial aspect of rationality: invariance, is violated. In addition, the contribution ex- plains Kahneman and Tversky’s Prospect Theory and illustrates their value function. Finally, it discusses the reversals of preference in framing and framing of contingen- cies. The framing manipulation is viewed as a public tool for influencing the decision maker’s private framing of the problem in terms of gains or losses, which determines the decision maker’s evaluation of the options. In conclusion, the psychology of choice is relevant both for the descriptive question of how decisions are made and for the nor- mative question of how decisions ought to be made.
{"title":"Economics and Psychology. The Framing of Decisions","authors":"Daniele Schilirò","doi":"10.14505//JMEF.V2.2(3).05","DOIUrl":"https://doi.org/10.14505//JMEF.V2.2(3).05","url":null,"abstract":"In the Theory of Rational Decision Making the psychological aspects are set aside. This contribution seeks to point out the relevance of psychology into eco- nomic decisions. The essay treats the “framing of decisions”, which is a pillar of Kahneman’s behavioral theory. Framing must be considered a special case of the more general phenomenon of dependency from the representation. The best-known risky choice-framing problem, i.e. the “Asian Disease Problem”, is shown where an essen- tial aspect of rationality: invariance, is violated. In addition, the contribution ex- plains Kahneman and Tversky’s Prospect Theory and illustrates their value function. Finally, it discusses the reversals of preference in framing and framing of contingen- cies. The framing manipulation is viewed as a public tool for influencing the decision maker’s private framing of the problem in terms of gains or losses, which determines the decision maker’s evaluation of the options. In conclusion, the psychology of choice is relevant both for the descriptive question of how decisions are made and for the nor- mative question of how decisions ought to be made.","PeriodicalId":367341,"journal":{"name":"Journal of Mathematical Economics and Finance","volume":"113 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2016-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125096798","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}
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