Pub Date : 2024-03-01DOI: 10.1080/15326349.2024.2319208
Erol A. Peköz, Rhonda Righter
In Gambler’s Ruin when both players start with the same amount of money, we show the playing time stochastically increases when the games are made more fair. We give two different arguments for thi...
{"title":"Increasing Gambler’s Ruin duration and Brownian motion exit times","authors":"Erol A. Peköz, Rhonda Righter","doi":"10.1080/15326349.2024.2319208","DOIUrl":"https://doi.org/10.1080/15326349.2024.2319208","url":null,"abstract":"In Gambler’s Ruin when both players start with the same amount of money, we show the playing time stochastically increases when the games are made more fair. We give two different arguments for thi...","PeriodicalId":21970,"journal":{"name":"Stochastic Models","volume":"3 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2024-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140019652","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-03-01DOI: 10.1080/15326349.2024.2321195
Bo Yang, Ruili Song, Dingjun Yao, Gongpin Cheng
This article focuses on the classic optimal dividend and reinsurance problems. Different from the existing literature, it assumes that the insurance company has two lines of business with a common ...
{"title":"Optimal dividend and proportional reinsurance strategy for the risk model with common shock dependence","authors":"Bo Yang, Ruili Song, Dingjun Yao, Gongpin Cheng","doi":"10.1080/15326349.2024.2321195","DOIUrl":"https://doi.org/10.1080/15326349.2024.2321195","url":null,"abstract":"This article focuses on the classic optimal dividend and reinsurance problems. Different from the existing literature, it assumes that the insurance company has two lines of business with a common ...","PeriodicalId":21970,"journal":{"name":"Stochastic Models","volume":"46 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2024-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140010140","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-02-05DOI: 10.1080/15326349.2024.2305344
Emmanuel Coffie
While the original Ait-Sahalia interest rate model has been found to be of considerable use for describing the time-series evolution of interest rates, it may not possess adequate specifications to...
{"title":"Numerical approximation of a hybrid Poisson-jump Ait-Sahalia-type interest rate model with delay","authors":"Emmanuel Coffie","doi":"10.1080/15326349.2024.2305344","DOIUrl":"https://doi.org/10.1080/15326349.2024.2305344","url":null,"abstract":"While the original Ait-Sahalia interest rate model has been found to be of considerable use for describing the time-series evolution of interest rates, it may not possess adequate specifications to...","PeriodicalId":21970,"journal":{"name":"Stochastic Models","volume":"7 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2024-02-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139754960","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-02-02DOI: 10.1080/15326349.2023.2297959
Igor Lazov, Petar Lazov
We consider a population of finite size M, where the current number N of entities, N∈{0,1,2,…,M}, determines its states. We geometrically analyze the amounts of information iN and iM−N, carried by ...
我们考虑一个有限大小为 M 的群体，当前实体的数量 N（N∈{0,1,2,...,M}）决定了它的状态。我们从几何学角度分析了 N 和 iM-N 所携带的信息量。
{"title":"Geometrical interpretation of the population entropy maximum","authors":"Igor Lazov, Petar Lazov","doi":"10.1080/15326349.2023.2297959","DOIUrl":"https://doi.org/10.1080/15326349.2023.2297959","url":null,"abstract":"We consider a population of finite size M, where the current number N of entities, N∈{0,1,2,…,M}, determines its states. We geometrically analyze the amounts of information iN and iM−N, carried by ...","PeriodicalId":21970,"journal":{"name":"Stochastic Models","volume":"38 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2024-02-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139664579","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-12-18DOI: 10.1080/15326349.2023.2286961
Miaomiao Wang, Shunping Zheng, Xuejun Wang
In this article, under some suitable conditions, we study the Lq convergence and complete q-th moment convergence for arrays of rowwise asymptotically almost negatively associated (AANA, for short)...
{"title":"Some convergence properties for arrays of rowwise asymptotically almost negatively associated random variables under sub-linear expectations","authors":"Miaomiao Wang, Shunping Zheng, Xuejun Wang","doi":"10.1080/15326349.2023.2286961","DOIUrl":"https://doi.org/10.1080/15326349.2023.2286961","url":null,"abstract":"In this article, under some suitable conditions, we study the Lq convergence and complete q-th moment convergence for arrays of rowwise asymptotically almost negatively associated (AANA, for short)...","PeriodicalId":21970,"journal":{"name":"Stochastic Models","volume":"26 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2023-12-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138745172","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-11-20DOI: 10.1080/15326349.2023.2278527
Pavel Ievlev
This article investigates the Parisian ruin probability for a class of Gaussian processes with power-asymmetric behavior of the variance near the unique optimal point. We derive the exact asymptoti...
{"title":"Parisian ruin with power-asymmetric variance near the optimal point with application to many-inputs proportional reinsurance","authors":"Pavel Ievlev","doi":"10.1080/15326349.2023.2278527","DOIUrl":"https://doi.org/10.1080/15326349.2023.2278527","url":null,"abstract":"This article investigates the Parisian ruin probability for a class of Gaussian processes with power-asymmetric behavior of the variance near the unique optimal point. We derive the exact asymptoti...","PeriodicalId":21970,"journal":{"name":"Stochastic Models","volume":"71 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2023-11-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138536195","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-11-16DOI: 10.1080/15326349.2023.2275298
Yuecai Han, Dingwen Zhang
In this article, we investigate the nonparametric Nadaraya-Watson estimator for the drift function of stochastic differential equations driven by fractional Brownian motion of the Hurst parameter H...
{"title":"Nadaraya-Watson estimators for stochastic differential equations driven by fractional Brownian motion","authors":"Yuecai Han, Dingwen Zhang","doi":"10.1080/15326349.2023.2275298","DOIUrl":"https://doi.org/10.1080/15326349.2023.2275298","url":null,"abstract":"In this article, we investigate the nonparametric Nadaraya-Watson estimator for the drift function of stochastic differential equations driven by fractional Brownian motion of the Hurst parameter H...","PeriodicalId":21970,"journal":{"name":"Stochastic Models","volume":"289 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2023-11-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138536258","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-10-26DOI: 10.1080/15326349.2023.2267644
Hongshuai Dai, Yanhua Wu
{"title":"A queueing model with ON/OFF sources: approximation and stationarity","authors":"Hongshuai Dai, Yanhua Wu","doi":"10.1080/15326349.2023.2267644","DOIUrl":"https://doi.org/10.1080/15326349.2023.2267644","url":null,"abstract":"","PeriodicalId":21970,"journal":{"name":"Stochastic Models","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134908742","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-10-19DOI: 10.1080/15326349.2023.2263538
Ji Hwan Cha, Maxim Finkelstein
Abstract.Populations of items continuously manufactured and incepted into operation are characterized by the corresponding distribution of a random age at each instant of chronological time. In this study, we consider heterogeneous populations with lifetime distributions indexed by a frailty parameter. Two approaches to defining the age composition for the described populations are described and the corresponding stochastic comparisons are considered.Keywords: Age compositionfrailtyheterogeneous populationsproduction ratestochastic comparisons2010 Mathematics Subject Classification:: 60H3 AcknowledgmentsThe authors greatly thank the reviewers for their helpful comments and advice, which have improved the presentation of this paper.Disclosure statementNo potential conflict of interest was reported by the authorsAdditional informationFundingThe work of the first author was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education (Grant Number: 2019R1A6A1A11051177). The work of the first author was also supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIP) (No. 2023R1A2C1003238).
{"title":"On age composition of dynamic heterogeneous populations","authors":"Ji Hwan Cha, Maxim Finkelstein","doi":"10.1080/15326349.2023.2263538","DOIUrl":"https://doi.org/10.1080/15326349.2023.2263538","url":null,"abstract":"Abstract.Populations of items continuously manufactured and incepted into operation are characterized by the corresponding distribution of a random age at each instant of chronological time. In this study, we consider heterogeneous populations with lifetime distributions indexed by a frailty parameter. Two approaches to defining the age composition for the described populations are described and the corresponding stochastic comparisons are considered.Keywords: Age compositionfrailtyheterogeneous populationsproduction ratestochastic comparisons2010 Mathematics Subject Classification:: 60H3 AcknowledgmentsThe authors greatly thank the reviewers for their helpful comments and advice, which have improved the presentation of this paper.Disclosure statementNo potential conflict of interest was reported by the authorsAdditional informationFundingThe work of the first author was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education (Grant Number: 2019R1A6A1A11051177). The work of the first author was also supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIP) (No. 2023R1A2C1003238).","PeriodicalId":21970,"journal":{"name":"Stochastic Models","volume":"9 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135730079","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-10-17DOI: 10.1080/15326349.2023.2267663
Pierre-Yves Louis, Meghdad Mirebrahimi
AbstractThe Pólya urn is the most representative example of a reinforced stochastic process. It leads to a random (non degenerated) time-limit. The Friedman urn is a natural generalization whose almost sure (a.s.) time-limit is not random any more. In this work, in the stream of previous recent works, we introduce a new family of (finite size) systems of reinforced stochastic processes, interacting through an additional collective reinforcement of mean field type. The two reinforcement rules strengths (one component-wise, one collective) are tuned through (possibly) two different rates. In special cases, these reinforcements are of Pólya or Friedman type as in urn contexts and may thus lead to limits which may be random or not. Different parameter regimes need to be considered. We state two kind of results. First, we study the time-asymptotic and show that L2 and a.s. convergence always holds. Moreover, all the components share the same time-limit (so called synchronization phenomenon). We study the nature of the limit (random/deterministic) according to the parameters’ regime considered. Second, we study fluctuations by proving central limit theorems. Scaling coefficients vary according to the regime considered. This gives insights into many different rates of convergence. In particular, we identify the regimes where synchronization is faster than convergence toward the shared time-limit.Keywords: Almost sure convergencecentral limit theoremsfluctuationsinteracting random systemsreinforced stochastic processesstable convergencesynchronization2010 Mathematics Subject Classification: Primary 60K35Primary 60F1560F05Secondary 62L20Secondary 62P35 AcknowledgmentsI would like to thank Professor Pierre-Yves Louis for introducing me to the problem and for all the useful comments and discussions. I am also very grateful for extremely constructive feedback from the referee.Disclosure statementNo potential conflict of interest was reported by the author(s).
{"title":"Synchronization and fluctuations for interacting stochastic systems with individual and collective reinforcement","authors":"Pierre-Yves Louis, Meghdad Mirebrahimi","doi":"10.1080/15326349.2023.2267663","DOIUrl":"https://doi.org/10.1080/15326349.2023.2267663","url":null,"abstract":"AbstractThe Pólya urn is the most representative example of a reinforced stochastic process. It leads to a random (non degenerated) time-limit. The Friedman urn is a natural generalization whose almost sure (a.s.) time-limit is not random any more. In this work, in the stream of previous recent works, we introduce a new family of (finite size) systems of reinforced stochastic processes, interacting through an additional collective reinforcement of mean field type. The two reinforcement rules strengths (one component-wise, one collective) are tuned through (possibly) two different rates. In special cases, these reinforcements are of Pólya or Friedman type as in urn contexts and may thus lead to limits which may be random or not. Different parameter regimes need to be considered. We state two kind of results. First, we study the time-asymptotic and show that L2 and a.s. convergence always holds. Moreover, all the components share the same time-limit (so called synchronization phenomenon). We study the nature of the limit (random/deterministic) according to the parameters’ regime considered. Second, we study fluctuations by proving central limit theorems. Scaling coefficients vary according to the regime considered. This gives insights into many different rates of convergence. In particular, we identify the regimes where synchronization is faster than convergence toward the shared time-limit.Keywords: Almost sure convergencecentral limit theoremsfluctuationsinteracting random systemsreinforced stochastic processesstable convergencesynchronization2010 Mathematics Subject Classification: Primary 60K35Primary 60F1560F05Secondary 62L20Secondary 62P35 AcknowledgmentsI would like to thank Professor Pierre-Yves Louis for introducing me to the problem and for all the useful comments and discussions. I am also very grateful for extremely constructive feedback from the referee.Disclosure statementNo potential conflict of interest was reported by the author(s).","PeriodicalId":21970,"journal":{"name":"Stochastic Models","volume":"71 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135944106","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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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