In this article, the valuation of firm’s present value in case of correlated defaults is studied. We showed that the valuation of portfolio credit risk can be interpreted as a valuation of the multiple contingent option. In this article, some results for valuation of multiple contingent options are generalized in case of stochastic barriers and the financial interpretation is given. Also, the modelling of other financial risks, notably, the market risk (the change of debt value) and the operational risk (the adequacy of selected credibility criteria) are included in these theorems. Using the principle of conservatism in credit risk assessment, the debtor credibility, the debt value and the firm value are assumed to follow geometric Wiener process.
{"title":"Present value of firm in case of correlated defaults","authors":"Mantas Valužis","doi":"10.15388/lmr.2006.30731","DOIUrl":"https://doi.org/10.15388/lmr.2006.30731","url":null,"abstract":"In this article, the valuation of firm’s present value in case of correlated defaults is studied. We showed that the valuation of portfolio credit risk can be interpreted as a valuation of the multiple contingent option. In this article, some results for valuation of multiple contingent options are generalized in case of stochastic barriers and the financial interpretation is given. Also, the modelling of other financial risks, notably, the market risk (the change of debt value) and the operational risk (the adequacy of selected credibility criteria) are included in these theorems. Using the principle of conservatism in credit risk assessment, the debtor credibility, the debt value and the firm value are assumed to follow geometric Wiener process.","PeriodicalId":33611,"journal":{"name":"Lietuvos Matematikos Rinkinys","volume":"38 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-09-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136238267","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":"Mathematics for business and management studies","authors":"Jovita Saldauskienė","doi":"10.15388/lmr.2006.30625","DOIUrl":"https://doi.org/10.15388/lmr.2006.30625","url":null,"abstract":"There is not abstract.","PeriodicalId":33611,"journal":{"name":"Lietuvos Matematikos Rinkinys","volume":"8 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-09-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136239006","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":"On Runge–Kutta-type methods for solving multidimensional stochastic differential equations","authors":"Jurgis Navikas","doi":"10.15388/lmr.2006.30800","DOIUrl":"https://doi.org/10.15388/lmr.2006.30800","url":null,"abstract":"There is not abstract.","PeriodicalId":33611,"journal":{"name":"Lietuvos Matematikos Rinkinys","volume":"342 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-09-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136238642","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":"On the uniform distribution of endomorphisms of s-dimensional torus, II","authors":"Birutė Kryžienė, Gintautas Misevičius","doi":"10.15388/lmr.2006.30565","DOIUrl":"https://doi.org/10.15388/lmr.2006.30565","url":null,"abstract":"There is not abstract.","PeriodicalId":33611,"journal":{"name":"Lietuvos Matematikos Rinkinys","volume":"159 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-09-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136239921","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}
The reflective study models are quite frequent and well analyzed in the scientific literature. Still their realization premises being different in many countries keep forming a scientific issue which needs a special attention, especially in learning mathematics. In this context there arises a problem question: what are the realization limitations of the traditional and reflective mathematics learning models?The research paper consists of two parts. The first part clears a problems of the realization a traditional study model. The second part clears out the possible realization limitations of the above mentioned model in Lithuanian context.
{"title":"Problems in realizing study models on mathematics","authors":"Regina Novikienė, Nijolė Čiučiulkienė","doi":"10.15388/lmr.2006.30614","DOIUrl":"https://doi.org/10.15388/lmr.2006.30614","url":null,"abstract":"The reflective study models are quite frequent and well analyzed in the scientific literature. Still their realization premises being different in many countries keep forming a scientific issue which needs a special attention, especially in learning mathematics. In this context there arises a problem question: what are the realization limitations of the traditional and reflective mathematics learning models?The research paper consists of two parts. The first part clears a problems of the realization a traditional study model. The second part clears out the possible realization limitations of the above mentioned model in Lithuanian context.
","PeriodicalId":33611,"journal":{"name":"Lietuvos Matematikos Rinkinys","volume":"3 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-09-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136239925","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}
Investigation of the threedirectional forced synhronization system, composed of four oscillators, is carried out. The exact expressions of the step responses functions for the synchronization system are derived and the transition process in the system is analysed.
{"title":"Trijų krypčių priverstinės sinchronizacijos sistemos matematinio modelio sudarymas ir tyrimas","authors":"Violeta Borsuk, Jonas Rimas","doi":"10.15388/lmr.2006.30753","DOIUrl":"https://doi.org/10.15388/lmr.2006.30753","url":null,"abstract":"Investigation of the threedirectional forced synhronization system, composed of four oscillators, is carried out. The exact expressions of the step responses functions for the synchronization system are derived and the transition process in the system is analysed.","PeriodicalId":33611,"journal":{"name":"Lietuvos Matematikos Rinkinys","volume":"24 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-09-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136240097","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}
The paper reviews the visualisation problems of genetic sequences and of their analysis results as well as other related problems. A possible formulation of the problem based on similarity, complexity measure (distance) between DNA sequences is proposed. It is solved by making use of multidimensional scaling (MDS) of principal component analysis (PCA) methods.
{"title":"Visualisation of nucleotide sequences","authors":"Tomas Rekašius","doi":"10.15388/lmr.2006.30765","DOIUrl":"https://doi.org/10.15388/lmr.2006.30765","url":null,"abstract":"The paper reviews the visualisation problems of genetic sequences and of their analysis results as well as other related problems. A possible formulation of the problem based on similarity, complexity measure (distance) between DNA sequences is proposed. It is solved by making use of multidimensional scaling (MDS) of principal component analysis (PCA) methods.","PeriodicalId":33611,"journal":{"name":"Lietuvos Matematikos Rinkinys","volume":"12 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-09-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136240102","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}
Several non-standard problems are regarded and the possibilities of simple approaching to their solution are regarded and discussed.
考虑了几个非标准问题，并对其简单逼近的可能性进行了考虑和讨论。
{"title":"More simple solution of not so simple problems – how does it happen?","authors":"Romualdas Kašuba","doi":"10.15388/lmr.2006.30604","DOIUrl":"https://doi.org/10.15388/lmr.2006.30604","url":null,"abstract":"Several non-standard problems are regarded and the possibilities of simple approaching to their solution are regarded and discussed.","PeriodicalId":33611,"journal":{"name":"Lietuvos Matematikos Rinkinys","volume":"76 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-09-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136240335","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}
The positioning problem considered in this paper is an attempt to find system’s of a few points position using accelerations. Today’s industry provides with various types of accelerometers suitable for acceleration measure. That data may be used to trace object movement.Final results showed that such movement trace is possible and may be applicable. The results also showed origins for errors which according to the results, are quite high globally. The final conclusion follows: the model created must be analized further in a deeper level, and error origins must be eliminated or at least minimized by either chosing different solving or modeling methods, either by revising used ones.
{"title":"Akselerometrų taikymo matematinis modelis","authors":"Vincas Benevičius, Narimantas Listopadskis","doi":"10.15388/lmr.2006.30741","DOIUrl":"https://doi.org/10.15388/lmr.2006.30741","url":null,"abstract":"The positioning problem considered in this paper is an attempt to find system’s of a few points position using accelerations. Today’s industry provides with various types of accelerometers suitable for acceleration measure. That data may be used to trace object movement.Final results showed that such movement trace is possible and may be applicable. The results also showed origins for errors which according to the results, are quite high globally. The final conclusion follows: the model created must be analized further in a deeper level, and error origins must be eliminated or at least minimized by either chosing different solving or modeling methods, either by revising used ones.","PeriodicalId":33611,"journal":{"name":"Lietuvos Matematikos Rinkinys","volume":"79 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-09-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136240343","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}
The Baltic States equity market is a challenge for investors and financial analysts. Unfortunately strong assivity is observed in ``young'' markets, therefore any (Gaussian, α-stable etc) distribution fitting tests (Anderson–Darling, Kolmogorov–Smirnov, etc.) are poorly applicable. Improvement based on mixed distributions is proposed and its adequacy in the Baltic States market is tested. In this paper we use Koutrouvelis goodness-of-fit test and modified χ2 test.
{"title":"Analysis of passivity problems in the baltic equity market","authors":"Igoris Belovas, Audrius Kabašinskas, Leonidas Sakalauskas","doi":"10.15388/lmr.2006.30729","DOIUrl":"https://doi.org/10.15388/lmr.2006.30729","url":null,"abstract":"The Baltic States equity market is a challenge for investors and financial analysts. Unfortunately strong assivity is observed in ``young'' markets, therefore any (Gaussian, α-stable etc) distribution fitting tests (Anderson–Darling, Kolmogorov–Smirnov, etc.) are poorly applicable. Improvement based on mixed distributions is proposed and its adequacy in the Baltic States market is tested. In this paper we use Koutrouvelis goodness-of-fit test and modified χ2 test.","PeriodicalId":33611,"journal":{"name":"Lietuvos Matematikos Rinkinys","volume":"42 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-09-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136240358","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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