Generalizing earlier work of Delbaen and Haezendonck for given compound renewal process $S$ under a probability measure $P$ we characterize all probability measures $Q$ on the domain of $P$ such that $Q$ and $P$ are progressively equivalent and $S$ remains a compound renewal process under $Q$. As a consequence, we prove that any compound renewal process can be converted into a compound Poisson process through a change of measures and we show how this approach is related to premium calculation principles.
{"title":"A characterization of equivalent martingale measures in a renewal risk model with applications to premium calculation principles","authors":"N. D. Macheras, Spyridon M. Tzaninis","doi":"10.15559/20-VMSTA148","DOIUrl":"https://doi.org/10.15559/20-VMSTA148","url":null,"abstract":"Generalizing earlier work of Delbaen and Haezendonck for given compound renewal process $S$ under a probability measure $P$ we characterize all probability measures $Q$ on the domain of $P$ such that $Q$ and $P$ are progressively equivalent and $S$ remains a compound renewal process under $Q$. As a consequence, we prove that any compound renewal process can be converted into a compound Poisson process through a change of measures and we show how this approach is related to premium calculation principles.","PeriodicalId":42685,"journal":{"name":"Modern Stochastics-Theory and Applications","volume":"1 1","pages":""},"PeriodicalIF":0.4,"publicationDate":"2017-07-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77957089","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}
Infinite divisibility of a class of two-dimensional vectors with components in the second Wiener chaos is studied. Necessary and sufficient conditions for infinite divisibility is presented as well as more easily verifiable sufficient conditions. The case where both components consist of a sum of two Gaussian squares is treated in more depth, and it is conjectured that such vectors are infinitely divisible.
{"title":"On infinite divisibility of a class of two-dimensional vectors in the second Wiener chaos","authors":"A. Basse-O’Connor, J. Pedersen, V. Rohde","doi":"10.15559/20-vmsta160","DOIUrl":"https://doi.org/10.15559/20-vmsta160","url":null,"abstract":"Infinite divisibility of a class of two-dimensional vectors with components in the second Wiener chaos is studied. Necessary and sufficient conditions for infinite divisibility is presented as well as more easily verifiable sufficient conditions. The case where both components consist of a sum of two Gaussian squares is treated in more depth, and it is conjectured that such vectors are infinitely divisible.","PeriodicalId":42685,"journal":{"name":"Modern Stochastics-Theory and Applications","volume":"24 1","pages":""},"PeriodicalIF":0.4,"publicationDate":"2017-05-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"91359552","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}
We prove moment inequalities for a class of functionals of i.i.d. random fields. We then derive rates in the central limit theorem for weighted sums of such randoms fields via an approximation by $m$-dependent random fields.
{"title":"Convergence rates in the central limit theorem for weighted sums of Bernoulli random fields","authors":"D. Giraudo","doi":"10.15559/18-VMSTA121","DOIUrl":"https://doi.org/10.15559/18-VMSTA121","url":null,"abstract":"We prove moment inequalities for a class of functionals of i.i.d. random fields. We then derive rates in the central limit theorem for weighted sums of such randoms fields via an approximation by $m$-dependent random fields.","PeriodicalId":42685,"journal":{"name":"Modern Stochastics-Theory and Applications","volume":"89 1","pages":""},"PeriodicalIF":0.4,"publicationDate":"2017-03-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89134825","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 aim of this work is to establish essential properties of spatial birth-and-death processes with general birth and death rates on ${mathbb{R}^{mathrm{d}}}$. Spatial birth-and-death processes with time dependent rates are obtained as solutions to certain stochastic equations. The existence, uniqueness, uniqueness in law and the strong Markov property of unique solutions are proven when the integral of the birth rate over ${mathbb{R}^{mathrm{d}}}$ grows not faster than linearly with the number of particles of the system. Martingale properties of the constructed process provide a rigorous connection to the heuristic generator. The pathwise behavior of an aggregation model is also studied. The probability of extinction and the growth rate of the number of particles under condition of nonextinction are estimated.
{"title":"Spatial birth-and-death processes with a finite number of particles","authors":"V. Bezborodov, L. Di Persio","doi":"10.15559/22-VMSTA203","DOIUrl":"https://doi.org/10.15559/22-VMSTA203","url":null,"abstract":"The aim of this work is to establish essential properties of spatial birth-and-death processes with general birth and death rates on ${mathbb{R}^{mathrm{d}}}$. Spatial birth-and-death processes with time dependent rates are obtained as solutions to certain stochastic equations. The existence, uniqueness, uniqueness in law and the strong Markov property of unique solutions are proven when the integral of the birth rate over ${mathbb{R}^{mathrm{d}}}$ grows not faster than linearly with the number of particles of the system. Martingale properties of the constructed process provide a rigorous connection to the heuristic generator.\u0000The pathwise behavior of an aggregation model is also studied. The probability of extinction and the growth rate of the number of particles under condition of nonextinction are estimated.","PeriodicalId":42685,"journal":{"name":"Modern Stochastics-Theory and Applications","volume":"1 1","pages":""},"PeriodicalIF":0.4,"publicationDate":"2015-07-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"72985526","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}
京公网安备 11010802042870号
京ICP备2023020795号-1
扫码关注我们
求助内容：
应助结果提醒方式：