{"title":"Dynamics of flows of a substance in a channel with a branch","authors":"T. Ivanova","doi":"10.1063/5.0040091","DOIUrl":"https://doi.org/10.1063/5.0040091","url":null,"abstract":"A model of flow of a substance in a part of a network that consists of a channel and a branch of this channel is discussed. In general this model can be based on differential or difference equations. In this text a difference equations model is considered and studied and it describes how amounts of a substance are distributed along the cells that form the studied part of the network. For the stationary case of motion of the substance a class of long-tail probability distributions is obtained. This class contains famous discrete probability distributions as particular cases. The discussed research has many applications. Several notes about the case of application of the model to channels of human migration are presented.","PeriodicalId":438189,"journal":{"name":"SEVENTH INTERNATIONAL CONFERENCE ON NEW TRENDS IN THE APPLICATIONS OF DIFFERENTIAL EQUATIONS IN SCIENCES (NTADES 2020)","volume":"109 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-02-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126378966","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":"Claim reserving estimation by using the chain ladder method","authors":"E. Raeva, V. Pavlov, Simona Georgieva","doi":"10.1063/5.0040192","DOIUrl":"https://doi.org/10.1063/5.0040192","url":null,"abstract":"The Chain Ladder Method (CLM) is a widely used method from the insurance companies in order to predict different types of future payments. These important calculations are done a several times in the year because they approximately predict how much will have to be paid for some claims in the different lines of business that are yet to be reported. This paper, in their first part, presents the use of the method to predict the sum of Incurred but not reported type of claims, also known as IBNR and Reported but not settled claims, also known as RBNS. In the second part CLM has been applied to predict reserves only for IBNR. This approach allows to occur in the future and how much money should be booked by the company into a reserve for this kind of future claims. Some numerical experiments have been presented.","PeriodicalId":438189,"journal":{"name":"SEVENTH INTERNATIONAL CONFERENCE ON NEW TRENDS IN THE APPLICATIONS OF DIFFERENTIAL EQUATIONS IN SCIENCES (NTADES 2020)","volume":"11 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-02-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121381507","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}