Pub Date : 2023-03-21DOI: 10.1007/s00780-023-00499-w
Xiao Chen, J. Choi, Kasper Larsen, Duane J. Seppi
{"title":"Price impact in Nash equilibria","authors":"Xiao Chen, J. Choi, Kasper Larsen, Duane J. Seppi","doi":"10.1007/s00780-023-00499-w","DOIUrl":"https://doi.org/10.1007/s00780-023-00499-w","url":null,"abstract":"","PeriodicalId":50447,"journal":{"name":"Finance and Stochastics","volume":"27 1","pages":"305 - 340"},"PeriodicalIF":1.7,"publicationDate":"2023-03-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45005737","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"经济学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-02-09DOI: 10.1080/17442508.2023.2176231
A. Almeida, F. Cipriano
ABSTRACT This article establishes a large deviation principle for a non-Newtonian fluid of differential type, filling a two-dimensional non-axisymmetric bounded domain with slip boundary conditions. More precisely, we show that the solutions of small stochastic white noise perturbations of the third grade fluid equations converges to the deterministic solution, as the intensity of the noise goes to zero. Moreover, this convergence has an exponential rate given by a suitable rate function. To establish such asymptotic result, we follow the weak convergence approach introduced by Budhiraja, Dupuis and Ellis.
{"title":"A large deviation principle for fluids of third grade","authors":"A. Almeida, F. Cipriano","doi":"10.1080/17442508.2023.2176231","DOIUrl":"https://doi.org/10.1080/17442508.2023.2176231","url":null,"abstract":"ABSTRACT This article establishes a large deviation principle for a non-Newtonian fluid of differential type, filling a two-dimensional non-axisymmetric bounded domain with slip boundary conditions. More precisely, we show that the solutions of small stochastic white noise perturbations of the third grade fluid equations converges to the deterministic solution, as the intensity of the noise goes to zero. Moreover, this convergence has an exponential rate given by a suitable rate function. To establish such asymptotic result, we follow the weak convergence approach introduced by Budhiraja, Dupuis and Ellis.","PeriodicalId":50447,"journal":{"name":"Finance and Stochastics","volume":"66 1","pages":"906 - 940"},"PeriodicalIF":1.7,"publicationDate":"2023-02-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89266272","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"经济学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-01-23DOI: 10.1080/17442508.2023.2167518
M. Dozzi, E. T. Kolkovska, J. López-Mimbela, Rim Touibi
We study the trajectorywise blowup behaviour of a semilinear partial differential equation that is driven by a mixture of multiplicative Brownian and fractional Brownian motion, modelling different types of random perturbations. The linear operator is supposed to have an eigenfunction of constant sign, and we show its influence, as well as the influence of its eigenvalue and of the other parameters of the equation, on the occurrence of a blowup in finite time of the solution. We give estimates for the probability of finite time blowup and of blowup before a given fixed time. Essential tools are the mild and weak form of an associated random partial differential equation.
{"title":"Large time behaviour of semilinear stochastic partial differential equations perturbed by a mixture of Brownian and fractional Brownian motions","authors":"M. Dozzi, E. T. Kolkovska, J. López-Mimbela, Rim Touibi","doi":"10.1080/17442508.2023.2167518","DOIUrl":"https://doi.org/10.1080/17442508.2023.2167518","url":null,"abstract":"We study the trajectorywise blowup behaviour of a semilinear partial differential equation that is driven by a mixture of multiplicative Brownian and fractional Brownian motion, modelling different types of random perturbations. The linear operator is supposed to have an eigenfunction of constant sign, and we show its influence, as well as the influence of its eigenvalue and of the other parameters of the equation, on the occurrence of a blowup in finite time of the solution. We give estimates for the probability of finite time blowup and of blowup before a given fixed time. Essential tools are the mild and weak form of an associated random partial differential equation.","PeriodicalId":50447,"journal":{"name":"Finance and Stochastics","volume":"58 1","pages":"1192 - 1217"},"PeriodicalIF":1.7,"publicationDate":"2023-01-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84210369","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"经济学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-01-16DOI: 10.1080/17442508.2023.2165399
A. Sengar, N. S. Upadhye
In this article, we define a convoluted fractional Poisson process of order k (CFPPoK), which is governed by the discrete convolution operator in the system of fractional differential equations. Next, we obtain its one-dimensional distribution by using the Laplace transform of its state probabilities. Various distributional properties, such as probability generating function, moment generating function and moments, are derived. A special case of CFPPoK, (say) convoluted Poisson process of order k (CPPoK) is studied and also established Martingale characterization for CPPoK. We further derive the covariance structure of CFPPoK and investigate the long-range dependence property.
{"title":"Convoluted fractional Poisson process of order k","authors":"A. Sengar, N. S. Upadhye","doi":"10.1080/17442508.2023.2165399","DOIUrl":"https://doi.org/10.1080/17442508.2023.2165399","url":null,"abstract":"In this article, we define a convoluted fractional Poisson process of order k (CFPPoK), which is governed by the discrete convolution operator in the system of fractional differential equations. Next, we obtain its one-dimensional distribution by using the Laplace transform of its state probabilities. Various distributional properties, such as probability generating function, moment generating function and moments, are derived. A special case of CFPPoK, (say) convoluted Poisson process of order k (CPPoK) is studied and also established Martingale characterization for CPPoK. We further derive the covariance structure of CFPPoK and investigate the long-range dependence property.","PeriodicalId":50447,"journal":{"name":"Finance and Stochastics","volume":"57 1","pages":"1170 - 1191"},"PeriodicalIF":1.7,"publicationDate":"2023-01-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85501284","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"经济学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-01-16DOI: 10.1080/17442508.2023.2165396
K. Dhanalakshmi, P. Balasubramaniam
This manuscript addresses the existence and exponential stability of impulsive fractional neutral stochastic integrodifferential equations (IFNSIDEs) driven by Poisson jump and fractional Brownian motion (fBm) with nonlocal conditions via the Mönch fixed point theorem. The sufficient conditions for stability results are derived based on the pth moment exponential stable with the help of new impulsive integral inequality. Finally, a numerical example is presented to illustrate the efficiency of the theoretical results with different Hurst index in .
{"title":"Exponential stability of impulsive fractional neutral stochastic integro-differential equations with nonlocal conditions","authors":"K. Dhanalakshmi, P. Balasubramaniam","doi":"10.1080/17442508.2023.2165396","DOIUrl":"https://doi.org/10.1080/17442508.2023.2165396","url":null,"abstract":"This manuscript addresses the existence and exponential stability of impulsive fractional neutral stochastic integrodifferential equations (IFNSIDEs) driven by Poisson jump and fractional Brownian motion (fBm) with nonlocal conditions via the Mönch fixed point theorem. The sufficient conditions for stability results are derived based on the pth moment exponential stable with the help of new impulsive integral inequality. Finally, a numerical example is presented to illustrate the efficiency of the theoretical results with different Hurst index in .","PeriodicalId":50447,"journal":{"name":"Finance and Stochastics","volume":"5 1","pages":"1260 - 1293"},"PeriodicalIF":1.7,"publicationDate":"2023-01-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75998286","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"经济学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-01-11DOI: 10.1080/17442508.2022.2164695
A. Kuczmaszewska
In this work there is considered complete convergence and complete moment convergence for widely negative orthant dependent random variables under the sub-linear expectations. The presented results concern the weighted sums of these random variables and extend the corresponding results in classical probability space to the case of sub-linear expectation space.
{"title":"Complete convergence and complete moment convergence for widely negative orthant dependent random variables under the sub-linear expectations","authors":"A. Kuczmaszewska","doi":"10.1080/17442508.2022.2164695","DOIUrl":"https://doi.org/10.1080/17442508.2022.2164695","url":null,"abstract":"In this work there is considered complete convergence and complete moment convergence for widely negative orthant dependent random variables under the sub-linear expectations. The presented results concern the weighted sums of these random variables and extend the corresponding results in classical probability space to the case of sub-linear expectation space.","PeriodicalId":50447,"journal":{"name":"Finance and Stochastics","volume":"11 1","pages":"1101 - 1119"},"PeriodicalIF":1.7,"publicationDate":"2023-01-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78120758","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"经济学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-01-10DOI: 10.1080/17442508.2023.2165398
Junfeng Liu
In this paper, we study the following nonlinear fractional stochastic partial differential equation where denotes the Markovian generator of a stable-like Feller process with variable order and is a measurable function. The forcing noise denoted by is a spatially inhomogeneous white noise. Under some assumptions on the catalytic measure of the inhomogeneous Brownian sheet , we study the moment bounds for the solution. As a byproduct, we prove that the solution is weakly full intermittent based on the moment estimates of the solution. We also study the Hölder regularity of the solution with respect to the temporal and spatial variables, respectively.
{"title":"Solving a nonlinear fractional SPDE with spatially inhomogeneous white noise","authors":"Junfeng Liu","doi":"10.1080/17442508.2023.2165398","DOIUrl":"https://doi.org/10.1080/17442508.2023.2165398","url":null,"abstract":"In this paper, we study the following nonlinear fractional stochastic partial differential equation where denotes the Markovian generator of a stable-like Feller process with variable order and is a measurable function. The forcing noise denoted by is a spatially inhomogeneous white noise. Under some assumptions on the catalytic measure of the inhomogeneous Brownian sheet , we study the moment bounds for the solution. As a byproduct, we prove that the solution is weakly full intermittent based on the moment estimates of the solution. We also study the Hölder regularity of the solution with respect to the temporal and spatial variables, respectively.","PeriodicalId":50447,"journal":{"name":"Finance and Stochastics","volume":"9 1","pages":"1218 - 1240"},"PeriodicalIF":1.7,"publicationDate":"2023-01-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89266625","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"经济学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-01-09DOI: 10.1080/17442508.2023.2165397
Zaiming Liu, Bingzhen Geng, Xinyue Man, Xinyu Liu
This paper considers a continuous-time bidimensional renewal risk model with subexponential claims. In this model, the claim size vectors and their inter-arrival times form a sequence of independent and identically distributed random vectors following some general dependence structures introduced by [T. Jiang, Y. Wang, Y. Chen and H. Xu, Uniform asymptotic estimate for finite-time ruin probabilities of a time-dependent bidimensional renewal model, Insur. Math. Econom. 64 (2015), pp. 45–53.]. We not only extend the results of [T. Jiang, Y. Wang, Y. Chen and H. Xu, Uniform asymptotic estimate for finite-time ruin probabilities of a time-dependent bidimensional renewal model, Insur. Math. Econom. 64 (2015), pp. 45–53.] under some weak conditions, but we also obtain an asymptotic estimate of the finite-time sum-ruin probability. Furthermore, when the distributions of claim sizes have nonzero lower Karamata indices, some explicit asymptotic formulas are established for the infinite-time ruin probabilities.
{"title":"Uniform asymptotics for ruin probabilities of a time-dependent bidimensional renewal risk model with dependent subexponential claims","authors":"Zaiming Liu, Bingzhen Geng, Xinyue Man, Xinyu Liu","doi":"10.1080/17442508.2023.2165397","DOIUrl":"https://doi.org/10.1080/17442508.2023.2165397","url":null,"abstract":"This paper considers a continuous-time bidimensional renewal risk model with subexponential claims. In this model, the claim size vectors and their inter-arrival times form a sequence of independent and identically distributed random vectors following some general dependence structures introduced by [T. Jiang, Y. Wang, Y. Chen and H. Xu, Uniform asymptotic estimate for finite-time ruin probabilities of a time-dependent bidimensional renewal model, Insur. Math. Econom. 64 (2015), pp. 45–53.]. We not only extend the results of [T. Jiang, Y. Wang, Y. Chen and H. Xu, Uniform asymptotic estimate for finite-time ruin probabilities of a time-dependent bidimensional renewal model, Insur. Math. Econom. 64 (2015), pp. 45–53.] under some weak conditions, but we also obtain an asymptotic estimate of the finite-time sum-ruin probability. Furthermore, when the distributions of claim sizes have nonzero lower Karamata indices, some explicit asymptotic formulas are established for the infinite-time ruin probabilities.","PeriodicalId":50447,"journal":{"name":"Finance and Stochastics","volume":"1 1","pages":"1147 - 1169"},"PeriodicalIF":1.7,"publicationDate":"2023-01-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83346228","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"经济学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-01-08DOI: 10.1080/17442508.2022.2164694
Yongxin Gao, Fan Yang
In this paper, we study a three-species predator-prey model with modified LG-Holling type II with Lévy jumps, and we take the competition among predators into consideration. First, We use an Ornstein-Uhlenbeck process to describe the environmental stochasticity and prove that there is a unique positive solution to the system by mathematical analysis skills such as comparison theorem. Futhermore, the extinction or persistence in the mean of each species under different conditions is obtained. Finally, some numerical simulations are carried out to support our main results.
{"title":"Persistence and extinction of a modified LG-Holling type II predator-prey model with two competitive predators and Lévy jumps","authors":"Yongxin Gao, Fan Yang","doi":"10.1080/17442508.2022.2164694","DOIUrl":"https://doi.org/10.1080/17442508.2022.2164694","url":null,"abstract":"In this paper, we study a three-species predator-prey model with modified LG-Holling type II with Lévy jumps, and we take the competition among predators into consideration. First, We use an Ornstein-Uhlenbeck process to describe the environmental stochasticity and prove that there is a unique positive solution to the system by mathematical analysis skills such as comparison theorem. Futhermore, the extinction or persistence in the mean of each species under different conditions is obtained. Finally, some numerical simulations are carried out to support our main results.","PeriodicalId":50447,"journal":{"name":"Finance and Stochastics","volume":"27 1","pages":"1241 - 1259"},"PeriodicalIF":1.7,"publicationDate":"2023-01-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82251855","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"经济学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-12-16DOI: 10.1007/s00780-022-00496-5
Martin Herdegen, David G. Hobson, Joseph Jerome
{"title":"The infinite-horizon investment–consumption problem for Epstein–Zin stochastic differential utility. II: Existence, uniqueness and verification for \u0000 \u0000 \u0000 \u0000 \u0000 ϑ\u0000 ∈\u0000 (\u0000 0\u0000 ,\u0000 1\u0000 )\u0000 \u0000 $vartheta in (0,1)$\u0000","authors":"Martin Herdegen, David G. Hobson, Joseph Jerome","doi":"10.1007/s00780-022-00496-5","DOIUrl":"https://doi.org/10.1007/s00780-022-00496-5","url":null,"abstract":"","PeriodicalId":50447,"journal":{"name":"Finance and Stochastics","volume":"27 1","pages":"159-188"},"PeriodicalIF":1.7,"publicationDate":"2022-12-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41727894","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"经济学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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