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Nonlinear and unbalanced urn models with two types of strategies: a stochastic approximation point of view 具有两种策略的非线性和不平衡瓮模型:随机逼近的观点
IF 1.1 3区 工程技术
Probability in the Engineering and Informational Sciences Pub Date : 2022-05-20 DOI: 10.1017/s0269964822000134
Soumaya Idriss
{"title":"Nonlinear and unbalanced urn models with two types of strategies: a stochastic approximation point of view","authors":"Soumaya Idriss","doi":"10.1017/s0269964822000134","DOIUrl":"https://doi.org/10.1017/s0269964822000134","url":null,"abstract":"\u0000 In this paper, we treat a nonlinear and unbalanced \u0000 \u0000 \u0000 $2$\u0000 \u0000 -color urn scheme, subjected to two different nonlinear drawing rules, depending on the color withdrawn. We prove a central limit theorem as well as a law of large numbers for the urn composition. We also give an estimate of the mean and variance of both types of balls.","PeriodicalId":54582,"journal":{"name":"Probability in the Engineering and Informational Sciences","volume":"105 1","pages":""},"PeriodicalIF":1.1,"publicationDate":"2022-05-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82088535","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Random multi-hooking networks 随机多钩子网络
IF 1.1 3区 工程技术
Probability in the Engineering and Informational Sciences Pub Date : 2022-05-02 DOI: 10.1017/s0269964822000523
K. R. Bhutani, Ravi Kalpathy, H. Mahmoud
{"title":"Random multi-hooking networks","authors":"K. R. Bhutani, Ravi Kalpathy, H. Mahmoud","doi":"10.1017/s0269964822000523","DOIUrl":"https://doi.org/10.1017/s0269964822000523","url":null,"abstract":"\u0000 We introduce a broad class of multi-hooking networks, wherein multiple copies of a seed are hooked at each step at random locations, and the number of copies follows a predetermined building sequence of numbers. We analyze the degree profile in random multi-hooking networks by tracking two kinds of node degrees—the local average degree of a specific node over time and the global overall average degree in the graph. The former experiences phases and the latter is invariant with respect to the type of building sequence and is somewhat similar to the average degree in the initial seed. We also discuss the expected number of nodes of the smallest degree. Additionally, we study distances in the network through the lens of the average total path length, the average depth of a node, the eccentricity of a node, and the diameter of the graph.","PeriodicalId":54582,"journal":{"name":"Probability in the Engineering and Informational Sciences","volume":"15 1","pages":""},"PeriodicalIF":1.1,"publicationDate":"2022-05-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88698274","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 2
PES volume 36 issue 2 Cover and Back matter PES第36卷第2期封面和封底
IF 1.1 3区 工程技术
Probability in the Engineering and Informational Sciences Pub Date : 2022-04-01 DOI: 10.1017/s0269964822000110
{"title":"PES volume 36 issue 2 Cover and Back matter","authors":"","doi":"10.1017/s0269964822000110","DOIUrl":"https://doi.org/10.1017/s0269964822000110","url":null,"abstract":"","PeriodicalId":54582,"journal":{"name":"Probability in the Engineering and Informational Sciences","volume":"24 1","pages":"b1 - b2"},"PeriodicalIF":1.1,"publicationDate":"2022-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78206532","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
PES volume 36 issue 2 Cover and Front matter PES第36卷第2期封面和封面问题
IF 1.1 3区 工程技术
Probability in the Engineering and Informational Sciences Pub Date : 2022-04-01 DOI: 10.1017/s0269964822000109
{"title":"PES volume 36 issue 2 Cover and Front matter","authors":"","doi":"10.1017/s0269964822000109","DOIUrl":"https://doi.org/10.1017/s0269964822000109","url":null,"abstract":"","PeriodicalId":54582,"journal":{"name":"Probability in the Engineering and Informational Sciences","volume":"67 1","pages":"f1 - f2"},"PeriodicalIF":1.1,"publicationDate":"2022-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74886606","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Joint moments of discounted claims and discounted perturbation until ruin in the compound Poisson risk model with diffusion 带扩散的复合泊松风险模型中索赔折现与扰动折现直至破产的联合矩
IF 1.1 3区 工程技术
Probability in the Engineering and Informational Sciences Pub Date : 2022-03-31 DOI: 10.1017/S0269964822000080
Eric C. K. Cheung, Haibo Liu
{"title":"Joint moments of discounted claims and discounted perturbation until ruin in the compound Poisson risk model with diffusion","authors":"Eric C. K. Cheung, Haibo Liu","doi":"10.1017/S0269964822000080","DOIUrl":"https://doi.org/10.1017/S0269964822000080","url":null,"abstract":"This paper studies a generalization of the Gerber-Shiu expected discounted penalty function [Gerber and Shiu (1998). On the time value of ruin. North American Actuarial Journal 2(1): 48–72] in the context of the perturbed compound Poisson insurance risk model, where the moments of the total discounted claims and the discounted small fluctuations (arising from the Brownian motion) until ruin are also included. In particular, the latter quantity is represented by a stochastic integral and has never been analyzed in the literature to the best of our knowledge. Recursive integro-differential equations satisfied by our generalized Gerber-Shiu function are derived, and these are transformed to defective renewal equations where the components are identified. Explicit solutions are given when the individual claim amounts are distributed as a combination of exponentials. Numerical illustrations are provided, including the computation of the covariance between discounted claims and discounted perturbation until ruin.","PeriodicalId":54582,"journal":{"name":"Probability in the Engineering and Informational Sciences","volume":"17 1","pages":"387 - 417"},"PeriodicalIF":1.1,"publicationDate":"2022-03-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87250436","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
An adaptive strategy for offering m-out-of-n insurance policies 提供m-out- n保险策略的自适应策略
IF 1.1 3区 工程技术
Probability in the Engineering and Informational Sciences Pub Date : 2022-03-15 DOI: 10.1017/S0269964821000504
G. S. Fishman, S. Stidham
{"title":"An adaptive strategy for offering m-out-of-n insurance policies","authors":"G. S. Fishman, S. Stidham","doi":"10.1017/S0269964821000504","DOIUrl":"https://doi.org/10.1017/S0269964821000504","url":null,"abstract":"A company with $n$ geographically widely dispersed sites seeks insurance that pays off if $m$ out of the $n$ sites experience rarely occurring catastrophes (e.g., earthquakes) during a year. This study describes an adaptive dynamic strategy that enables an insurance company to offer the policy with smaller loss probability than more conventional static policies induce, but at a comparable or lower premium. The strategy accomplishes this by periodically purchasing reinsurance on individual sites. Exploiting rarity, the policy induces zero loss with probability one if no more than one quake occurs during any review interval. The policy also may induce a profit if $m$ or more quakes occur in an interval if no quakes have occurred in previous intervals. The study also examines the benefit of more than one reinsurance policy per active site. The study relies on expected utility to determine indifference premiums and derives an upper bound on loss probability independent of premium.","PeriodicalId":54582,"journal":{"name":"Probability in the Engineering and Informational Sciences","volume":"1 1","pages":"106 - 134"},"PeriodicalIF":1.1,"publicationDate":"2022-03-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86470075","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Optimal management and valuation of a natural resource: the case of optimal harvesting 自然资源的最优管理和估价:最优收获的案例
IF 1.1 3区 工程技术
Probability in the Engineering and Informational Sciences Pub Date : 2022-03-11 DOI: 10.1017/s0269964822000043
M'hamed Gaïgi, Idris Kharroubi, T. Lim
{"title":"Optimal management and valuation of a natural resource: the case of optimal harvesting","authors":"M'hamed Gaïgi, Idris Kharroubi, T. Lim","doi":"10.1017/s0269964822000043","DOIUrl":"https://doi.org/10.1017/s0269964822000043","url":null,"abstract":"\u0000 In this paper, we consider the problem of sustainable harvesting. We explain how the manager maximizes his/her profit according to the quantity of natural resource available in a harvesting area and under the constraint of penalties and fines when the quota is exceeded. We characterize the optimal values and some optimal strategies using a verification result. We then show by numerical examples that this optimal strategy is better than naive ones. Moreover, we define a level of fines which insures the double objective of the sustainable harvesting: a remaining quantity of available natural resource to insure its sustainability and an acceptable income for the manager.","PeriodicalId":54582,"journal":{"name":"Probability in the Engineering and Informational Sciences","volume":"9 1","pages":""},"PeriodicalIF":1.1,"publicationDate":"2022-03-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86695968","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Credit default swap pricing with counterparty risk in a reduced form model with a common jump process 信用违约掉期定价与交易对手风险的简化模型与共同跳跃过程
IF 1.1 3区 工程技术
Probability in the Engineering and Informational Sciences Pub Date : 2022-02-22 DOI: 10.1017/S0269964822000018
Yu Chen, Yu Xing
{"title":"Credit default swap pricing with counterparty risk in a reduced form model with a common jump process","authors":"Yu Chen, Yu Xing","doi":"10.1017/S0269964822000018","DOIUrl":"https://doi.org/10.1017/S0269964822000018","url":null,"abstract":"Abstract In this paper, we study the credit default swap (CDS) pricing with counterparty risk in a reduced form model. The default jump intensities of the reference firm and counterparty are both assumed to follow the mean-reverting CIR processes with independent jumps respectively and a common jump. The approximate closed-form solutions of the joint survival probability density and the probability density of the first default can be obtained by using the PDE method. Then with the expressions of the probability densities, we can get the formula for the CDS price with counterparty risk in a reduced form model with a common jump. In the numerical analysis part, we find that the default of the reference asset has a greater impact on the CDS price than that of the default of counterparty after introducing the common jump process.","PeriodicalId":54582,"journal":{"name":"Probability in the Engineering and Informational Sciences","volume":"56 1","pages":"275 - 293"},"PeriodicalIF":1.1,"publicationDate":"2022-02-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"91298464","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
On reconsidering entropies and divergences and their cumulative counterparts: Csiszár's, DPD's and Fisher's type cumulative and survival measures 重新考虑熵和散度及其累积对等物:Csiszár’s、DPD’s和Fisher’s型累积和生存度量
IF 1.1 3区 工程技术
Probability in the Engineering and Informational Sciences Pub Date : 2022-02-21 DOI: 10.1017/S0269964822000031
K. Zografos
{"title":"On reconsidering entropies and divergences and their cumulative counterparts: Csiszár's, DPD's and Fisher's type cumulative and survival measures","authors":"K. Zografos","doi":"10.1017/S0269964822000031","DOIUrl":"https://doi.org/10.1017/S0269964822000031","url":null,"abstract":"This paper concentrates on the fundamental concepts of entropy, information and divergence to the case where the distribution function and the respective survival function play the central role in their definition. The main aim is to provide an overview of these three categories of measures of information and their cumulative and survival counterparts. It also aims to introduce and discuss Csiszár's type cumulative and survival divergences and the analogous Fisher's type information on the basis of cumulative and survival functions.","PeriodicalId":54582,"journal":{"name":"Probability in the Engineering and Informational Sciences","volume":"14 1","pages":"294 - 321"},"PeriodicalIF":1.1,"publicationDate":"2022-02-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73511879","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
Optimal call center forecasting and staffing 优化呼叫中心预测和人员配置
IF 1.1 3区 工程技术
Probability in the Engineering and Informational Sciences Pub Date : 2022-02-16 DOI: 10.1017/S0269964820000595
Sihan Ding, G. Koole
{"title":"Optimal call center forecasting and staffing","authors":"Sihan Ding, G. Koole","doi":"10.1017/S0269964820000595","DOIUrl":"https://doi.org/10.1017/S0269964820000595","url":null,"abstract":"Abstract In this paper, we consider a two-stage call center staffing model. In the first stage, the interval staffing levels are set under arrival rate uncertainty. In the second stage, these initial staffing levels are corrected to the right value based on more precise arrival rate information. We show that this problem is of newsvendor type, where the costs are the initial staffing costs plus the second stage adaptation costs. We show that we should initially staff according to a quantile of the distributional forecast, rather than the mean. It is also shown that the errors in staffing are approximately linear in the forecasting errors. This leads to the conclusion that the weighted sum of errors should be the error measurement in call center forecasting, since minimizing, it minimizes the total staffing costs. In special cases where the costs are symmetric for over- and understaffing, this is equivalent to minimizing the weighted absolute percentage error.","PeriodicalId":54582,"journal":{"name":"Probability in the Engineering and Informational Sciences","volume":"26 1","pages":"254 - 263"},"PeriodicalIF":1.1,"publicationDate":"2022-02-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85288626","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 2
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