Pub Date : 2022-07-14DOI: 10.1017/S0269964822000195
Dechen Gao, Kristina P. Sendova
In this paper, we discuss a generalization of the classical compound Poisson model with claim sizes following a compound distribution. As applications, we consider models involving zero-truncated geometric, zero-truncated negative-binomial and zero-truncated binomial batch-claim arrivals. We also provide some ruin-related quantities under the resulting risk models. Finally, through numerical examples, we visualize the behavior of these quantities.
{"title":"Applications of the classical compound Poisson model with claim sizes following a compound distribution","authors":"Dechen Gao, Kristina P. Sendova","doi":"10.1017/S0269964822000195","DOIUrl":"https://doi.org/10.1017/S0269964822000195","url":null,"abstract":"In this paper, we discuss a generalization of the classical compound Poisson model with claim sizes following a compound distribution. As applications, we consider models involving zero-truncated geometric, zero-truncated negative-binomial and zero-truncated binomial batch-claim arrivals. We also provide some ruin-related quantities under the resulting risk models. Finally, through numerical examples, we visualize the behavior of these quantities.","PeriodicalId":54582,"journal":{"name":"Probability in the Engineering and Informational Sciences","volume":"3 1","pages":"357 - 386"},"PeriodicalIF":1.1,"publicationDate":"2022-07-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76603430","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}
Pub Date : 2022-07-08DOI: 10.1017/s0269964822000225
Akash Sharma, Chanchal Kundu
Recently, there is a growing interest to study the variability of uncertainty measure in information theory. For the sake of analyzing such interest, varentropy has been introduced and examined for one-sided truncated random variables. As the interval entropy measure is instrumental in summarizing various system and its components properties when it fails between two time points, exploring variability of such measure pronounces the extracted information. In this article, we introduce the concept of varentropy for doubly truncated random variable. A detailed study of theoretical results taking into account transformations, monotonicity and other conditions is proposed. A simulation study has been carried out to investigate the behavior of varentropy in shrinking interval for simulated and real-life data sets. Furthermore, applications related to the choice of most acceptable system and the first-passage times of an Ornstein–Uhlenbeck jump-diffusion process are illustrated.
{"title":"Varentropy of doubly truncated random variable","authors":"Akash Sharma, Chanchal Kundu","doi":"10.1017/s0269964822000225","DOIUrl":"https://doi.org/10.1017/s0269964822000225","url":null,"abstract":"Recently, there is a growing interest to study the variability of uncertainty measure in information theory. For the sake of analyzing such interest, varentropy has been introduced and examined for one-sided truncated random variables. As the interval entropy measure is instrumental in summarizing various system and its components properties when it fails between two time points, exploring variability of such measure pronounces the extracted information. In this article, we introduce the concept of varentropy for doubly truncated random variable. A detailed study of theoretical results taking into account transformations, monotonicity and other conditions is proposed. A simulation study has been carried out to investigate the behavior of varentropy in shrinking interval for simulated and real-life data sets. Furthermore, applications related to the choice of most acceptable system and the first-passage times of an Ornstein–Uhlenbeck jump-diffusion process are illustrated.","PeriodicalId":54582,"journal":{"name":"Probability in the Engineering and Informational Sciences","volume":"12 1","pages":""},"PeriodicalIF":1.1,"publicationDate":"2022-07-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79617892","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}
Pub Date : 2022-07-01DOI: 10.1017/s0269964822000274
{"title":"PES volume 36 issue 3 Cover and Front matter","authors":"","doi":"10.1017/s0269964822000274","DOIUrl":"https://doi.org/10.1017/s0269964822000274","url":null,"abstract":"","PeriodicalId":54582,"journal":{"name":"Probability in the Engineering and Informational Sciences","volume":"72 1","pages":"f1 - f2"},"PeriodicalIF":1.1,"publicationDate":"2022-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75374147","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}
Pub Date : 2022-07-01DOI: 10.1017/s0269964822000262
{"title":"PES volume 36 issue 3 Cover and Back matter","authors":"","doi":"10.1017/s0269964822000262","DOIUrl":"https://doi.org/10.1017/s0269964822000262","url":null,"abstract":"","PeriodicalId":54582,"journal":{"name":"Probability in the Engineering and Informational Sciences","volume":"57 1","pages":"b1 - b2"},"PeriodicalIF":1.1,"publicationDate":"2022-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84757018","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}
Pub Date : 2022-06-23DOI: 10.1017/s0269964822000201
Wan-Yi Chiu
This paper examines the value-at-risk (VaR) implications of mean-variance hedging. We derive an equivalence between the VaR-based hedge and the mean-variance hedging. This method transfers the investor's subjective risk-aversion coefficient into the estimated VaR measure. As a result, we characterize the collapse probability bounds under which the VaR-based hedge could be insignificantly different from the minimum-variance hedge in the presence of estimation risk. The results indicate that the squared information ratio of futures returns is the primary factor determining the difference between the minimum-variance and VaR-based hedges.
{"title":"A value-at-risk approach to futures hedge","authors":"Wan-Yi Chiu","doi":"10.1017/s0269964822000201","DOIUrl":"https://doi.org/10.1017/s0269964822000201","url":null,"abstract":"\u0000 This paper examines the value-at-risk (VaR) implications of mean-variance hedging. We derive an equivalence between the VaR-based hedge and the mean-variance hedging. This method transfers the investor's subjective risk-aversion coefficient into the estimated VaR measure. As a result, we characterize the collapse probability bounds under which the VaR-based hedge could be insignificantly different from the minimum-variance hedge in the presence of estimation risk. The results indicate that the squared information ratio of futures returns is the primary factor determining the difference between the minimum-variance and VaR-based hedges.","PeriodicalId":54582,"journal":{"name":"Probability in the Engineering and Informational Sciences","volume":"51 1","pages":""},"PeriodicalIF":1.1,"publicationDate":"2022-06-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75072681","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}
Pub Date : 2022-06-10DOI: 10.1017/s0269964822000183
He Yi, N. Balakrishnan, Xiang Li
In this paper, the multi-state survival signature is first redefined for multi-state coherent or mixed systems with independent and identically distributed (i.i.d.) multi-state components. With the assumption of independence of component lifetimes at different state levels, transformation formulas of multi-state survival signatures of different sizes are established through the use of equivalent systems and a generalized triangle rule for order statistics from several independent and non-identical distributions. The results obtained facilitate stochastic comparisons of multi-state coherent or mixed systems with different numbers of i.i.d. multi-state components. Specific examples are finally presented to illustrate the transformation formulas established here, and also their use in comparing systems of different sizes.
{"title":"Equivalency of multi-state survival signatures of multi-state systems of different sizes and its use in the comparison of systems","authors":"He Yi, N. Balakrishnan, Xiang Li","doi":"10.1017/s0269964822000183","DOIUrl":"https://doi.org/10.1017/s0269964822000183","url":null,"abstract":"In this paper, the multi-state survival signature is first redefined for multi-state coherent or mixed systems with independent and identically distributed (i.i.d.) multi-state components. With the assumption of independence of component lifetimes at different state levels, transformation formulas of multi-state survival signatures of different sizes are established through the use of equivalent systems and a generalized triangle rule for order statistics from several independent and non-identical distributions. The results obtained facilitate stochastic comparisons of multi-state coherent or mixed systems with different numbers of i.i.d. multi-state components. Specific examples are finally presented to illustrate the transformation formulas established here, and also their use in comparing systems of different sizes.","PeriodicalId":54582,"journal":{"name":"Probability in the Engineering and Informational Sciences","volume":"7 1","pages":""},"PeriodicalIF":1.1,"publicationDate":"2022-06-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78470632","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}
Pub Date : 2022-06-06DOI: 10.1017/S0269964822000092
Jiayi Xie, Wenguang Yu, Zhimin Zhang, Zhenyu Cui
In this paper, the classical compound Poisson model under periodic observation is studied. Different from the random observation assumption widely used in the literature, we suppose that the inter-observation time is a constant. In this model, both the finite-time and infinite-time Gerber-Shiu functions are studied via the Laguerre series expansion method. We show that the expansion coefficients can be recursively determined and also analyze the approximation errors in detail. Numerical results for several claim size density functions are given to demonstrate effectiveness of our method, and the effect of some parameters is also studied.
{"title":"Gerber-Shiu analysis in the compound Poisson model with constant inter-observation times","authors":"Jiayi Xie, Wenguang Yu, Zhimin Zhang, Zhenyu Cui","doi":"10.1017/S0269964822000092","DOIUrl":"https://doi.org/10.1017/S0269964822000092","url":null,"abstract":"In this paper, the classical compound Poisson model under periodic observation is studied. Different from the random observation assumption widely used in the literature, we suppose that the inter-observation time is a constant. In this model, both the finite-time and infinite-time Gerber-Shiu functions are studied via the Laguerre series expansion method. We show that the expansion coefficients can be recursively determined and also analyze the approximation errors in detail. Numerical results for several claim size density functions are given to demonstrate effectiveness of our method, and the effect of some parameters is also studied.","PeriodicalId":54582,"journal":{"name":"Probability in the Engineering and Informational Sciences","volume":"17 1","pages":"324 - 356"},"PeriodicalIF":1.1,"publicationDate":"2022-06-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79624567","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}
Pub Date : 2022-06-06DOI: 10.1017/s026996482200016x
S. Chadjiconstantinidis, G. Tzavelas
Sequences of non-decreasing (non-increasing) lower (upper) bounds for the renewal-type equation as well as for the renewal function which are improvements of the famous corresponding bounds of Marshal [(1973). Linear bounds on the renewal function. SIAM Journal on Applied Mathematics 24(2): 245–250] are given. Also, sequences such bounds converging to the ordinary renewal function are obtained for several reliability classes of the lifetime distributions of the inter-arrival times, which are refinements of all of the existing known corresponding bounds. For the first time, a lower bound for the renewal function with DMRL lifetimes is given. Finally, sequences of such improved bounds are given for the ordinary renewal density as well as for the right-tail of the distribution of the forward recurrence time.
{"title":"Improved bounds for the solutions of renewal equations","authors":"S. Chadjiconstantinidis, G. Tzavelas","doi":"10.1017/s026996482200016x","DOIUrl":"https://doi.org/10.1017/s026996482200016x","url":null,"abstract":"Sequences of non-decreasing (non-increasing) lower (upper) bounds for the renewal-type equation as well as for the renewal function which are improvements of the famous corresponding bounds of Marshal [(1973). Linear bounds on the renewal function. SIAM Journal on Applied Mathematics 24(2): 245–250] are given. Also, sequences such bounds converging to the ordinary renewal function are obtained for several reliability classes of the lifetime distributions of the inter-arrival times, which are refinements of all of the existing known corresponding bounds. For the first time, a lower bound for the renewal function with DMRL lifetimes is given. Finally, sequences of such improved bounds are given for the ordinary renewal density as well as for the right-tail of the distribution of the forward recurrence time.","PeriodicalId":54582,"journal":{"name":"Probability in the Engineering and Informational Sciences","volume":"2 1","pages":""},"PeriodicalIF":1.1,"publicationDate":"2022-06-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83123305","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}
Pub Date : 2022-05-26DOI: 10.1017/s0269964822000171
K. Preethi, A. Shophia Lawrence, B. Sivakumar
In this article, we provide a comprehensive analyses of two continuous review lost sales inventory system based on different replenishment policies, namely $(s,S)$ and $(s,Q)$ . We assume that the arrival times of demands form a Poisson process and that the demand sizes have i.i.d. exponential distribution. We assume that the items in stock may obsolete after an exponential time. The lead time for replenishment is exponential. We also assume that the excess demands and the demands that occurred during stock out periods are lost. Using the system point method of level crossing and integral equation method, we derive the steady-state probability distribution of inventory level explicitly. After deriving some system performance measures, we computed the total expected cost rate. We also provide numerical examples of sensitivity analyses involving different parameters and costs. As a result of our numerical analysis, we provide several insights on the optimal $(s,S)$ and $(s,Q)$ policies for inventory systems of obsolescence items with positive lead times. The better policy for maintaining inventory can be quantified numerically.
{"title":"Lost sales obsolescence inventory systems with positive lead time: a system-point level-crossing approach","authors":"K. Preethi, A. Shophia Lawrence, B. Sivakumar","doi":"10.1017/s0269964822000171","DOIUrl":"https://doi.org/10.1017/s0269964822000171","url":null,"abstract":"\u0000 In this article, we provide a comprehensive analyses of two continuous review lost sales inventory system based on different replenishment policies, namely \u0000 \u0000 \u0000 $(s,S)$\u0000 \u0000 and \u0000 \u0000 \u0000 $(s,Q)$\u0000 \u0000 . We assume that the arrival times of demands form a Poisson process and that the demand sizes have i.i.d. exponential distribution. We assume that the items in stock may obsolete after an exponential time. The lead time for replenishment is exponential. We also assume that the excess demands and the demands that occurred during stock out periods are lost. Using the system point method of level crossing and integral equation method, we derive the steady-state probability distribution of inventory level explicitly. After deriving some system performance measures, we computed the total expected cost rate. We also provide numerical examples of sensitivity analyses involving different parameters and costs. As a result of our numerical analysis, we provide several insights on the optimal \u0000 \u0000 \u0000 $(s,S)$\u0000 \u0000 and \u0000 \u0000 \u0000 $(s,Q)$\u0000 \u0000 policies for inventory systems of obsolescence items with positive lead times. The better policy for maintaining inventory can be quantified numerically.","PeriodicalId":54582,"journal":{"name":"Probability in the Engineering and Informational Sciences","volume":"1 1","pages":""},"PeriodicalIF":1.1,"publicationDate":"2022-05-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78425221","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}
{"title":"On approximation of the analytic fixed finite time large t probability distributions in an extreme renewal process with no-mean inter-renewals","authors":"P. H. Brill, M. Huang","doi":"10.1017/s0269964822000122","DOIUrl":"https://doi.org/10.1017/s0269964822000122","url":null,"abstract":"We consider an extreme renewal process with no-mean heavy-tailed Pareto(II) inter-renewals and shape parameter \u0000 \u0000 \u0000 $alpha$\u0000 \u0000 where \u0000 \u0000 \u0000 $0<alpha leq 1$\u0000 \u0000 . Two steps are required to derive integral expressions for the analytic probability density functions (pdfs) of the fixed finite time \u0000 \u0000 \u0000 $t$\u0000 \u0000 excess, age, and total life, and require extensive computations. Step 1 creates and solves a Volterra integral equation of the second kind for the limiting pdf of a basic underlying regenerative process defined in the text, which is used for all three fixed finite time \u0000 \u0000 \u0000 $t$\u0000 \u0000 pdfs. Step 2 builds the aforementioned integral expressions based on the limiting pdf in the basic underlying regenerative process. The limiting pdfs of the fixed finite time \u0000 \u0000 \u0000 $t$\u0000 \u0000 pdfs as \u0000 \u0000 \u0000 $trightarrow infty$\u0000 \u0000 do not exist. To reasonably observe the large \u0000 \u0000 \u0000 $t$\u0000 \u0000 pdfs in the extreme renewal process, we approximate them using the limiting pdfs having simple well-known formulas, in a companion renewal process where inter-renewals are right-truncated Pareto(II) variates with finite mean; this does not involve any computations. The distance between the approximating limiting pdfs and the analytic fixed finite time large \u0000 \u0000 \u0000 $t$\u0000 \u0000 pdfs is given by an \u0000 \u0000 \u0000 $L_{1}$\u0000 \u0000 metric taking values in \u0000 \u0000 \u0000 $(0,1)$\u0000 \u0000 , where “near \u0000 \u0000 \u0000 $0$\u0000 \u0000 ” means “close” and “near \u0000 \u0000 \u0000 $1$\u0000 \u0000 ” means “far”.","PeriodicalId":54582,"journal":{"name":"Probability in the Engineering and Informational Sciences","volume":"52 1","pages":""},"PeriodicalIF":1.1,"publicationDate":"2022-05-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84485473","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}
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