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An almost sure central limit theorem for the parabolic Anderson model with delta initial condition 初值为δ的抛物型Anderson模型的一个几乎确定的中心极限定理
IF 1.7 2区 经济学
Finance and Stochastics Pub Date : 2022-06-17 DOI: 10.1080/17442508.2022.2088236
Jingyu Li, Yong Zhang
{"title":"An almost sure central limit theorem for the parabolic Anderson model with delta initial condition","authors":"Jingyu Li, Yong Zhang","doi":"10.1080/17442508.2022.2088236","DOIUrl":"https://doi.org/10.1080/17442508.2022.2088236","url":null,"abstract":"Consider the parabolic Anderson model of the form , where for t>0 and with , and η is a centered Gaussian noise that is white in time and has a spatially homogeneous covariance given by a nonnegative-definite measure f that satisfies Dalang's condition. Let denote the standard Gaussian heat kernel on and set for all t>0 and . In this paper, we present an almost sure central limit theorem (ASCLT) and a functional ASCLT for spatial averages of the form as for fixed t>0 based on the quantitative analysis of f. In particular, when f is given by a Riesz kernel, that is, for some , we can also obtain the ASCLT.","PeriodicalId":50447,"journal":{"name":"Finance and Stochastics","volume":"1 1","pages":"483 - 500"},"PeriodicalIF":1.7,"publicationDate":"2022-06-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88667565","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}
引用次数: 3
Forward-backward doubly stochastic systems and classical solutions of path-dependent stochastic PDEs 正反向双随机系统及路径相关随机偏微分方程经典解
IF 1.7 2区 经济学
Finance and Stochastics Pub Date : 2022-06-11 DOI: 10.1080/17442508.2022.2085503
Yufeng Shi, Jiaqiang Wen, J. Xiong
{"title":"Forward-backward doubly stochastic systems and classical solutions of path-dependent stochastic PDEs","authors":"Yufeng Shi, Jiaqiang Wen, J. Xiong","doi":"10.1080/17442508.2022.2085503","DOIUrl":"https://doi.org/10.1080/17442508.2022.2085503","url":null,"abstract":"In this paper, a class of non-Markovian forward-backward doubly stochastic systems is studied. By using the technique of functional Itô (or path-dependent) calculus, the relationship between the systems and related path-dependent quasi-linear stochastic partial differential equations (SPDEs in short) is established, and the well-known nonlinear stochastic Feynman-Kac formula of Pardoux and Peng [Backward doubly stochastic differential equations and systems of quasilinear SPDEs, Probab. Theory Relat. Fields 98 (1994), pp. 209–227.] is developed to the non-Markovian situation. Moreover, we obtain the differentiability of the solution to the forward-backward doubly stochastic systems and some properties of solutions to the path-dependent SPDEs.","PeriodicalId":50447,"journal":{"name":"Finance and Stochastics","volume":"10 1","pages":"396 - 422"},"PeriodicalIF":1.7,"publicationDate":"2022-06-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87970437","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}
引用次数: 0
Solving optimal stopping problems under model uncertainty via empirical dual optimisation 基于经验对偶优化求解模型不确定性下的最优停车问题
IF 1.7 2区 经济学
Finance and Stochastics Pub Date : 2022-06-10 DOI: 10.1007/s00780-022-00480-z
D. Belomestny, Tobias Hübner, Volker Krätschmer
{"title":"Solving optimal stopping problems under model uncertainty via empirical dual optimisation","authors":"D. Belomestny, Tobias Hübner, Volker Krätschmer","doi":"10.1007/s00780-022-00480-z","DOIUrl":"https://doi.org/10.1007/s00780-022-00480-z","url":null,"abstract":"","PeriodicalId":50447,"journal":{"name":"Finance and Stochastics","volume":"26 1","pages":"461 - 503"},"PeriodicalIF":1.7,"publicationDate":"2022-06-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48912827","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}
引用次数: 0
Market-to-book ratio in stochastic portfolio theory 随机投资组合理论中的市净率
IF 1.7 2区 经济学
Finance and Stochastics Pub Date : 2022-06-08 DOI: 10.1007/s00780-023-00501-5
Donghan Kim
{"title":"Market-to-book ratio in stochastic portfolio theory","authors":"Donghan Kim","doi":"10.1007/s00780-023-00501-5","DOIUrl":"https://doi.org/10.1007/s00780-023-00501-5","url":null,"abstract":"","PeriodicalId":50447,"journal":{"name":"Finance and Stochastics","volume":"1 1","pages":"1 - 34"},"PeriodicalIF":1.7,"publicationDate":"2022-06-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46978331","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}
引用次数: 3
Convergence of densities of spatial averages of the parabolic Anderson model driven by colored noise 彩色噪声驱动下抛物型Anderson模型空间平均密度的收敛性
IF 1.7 2区 经济学
Finance and Stochastics Pub Date : 2022-05-27 DOI: 10.1080/17442508.2023.2238954
Sefika Kuzgun, D. Nualart
{"title":"Convergence of densities of spatial averages of the parabolic Anderson model driven by colored noise","authors":"Sefika Kuzgun, D. Nualart","doi":"10.1080/17442508.2023.2238954","DOIUrl":"https://doi.org/10.1080/17442508.2023.2238954","url":null,"abstract":"In this paper, we present a rate of convergence in the uniform norm for the densities of spatial averages of the solution to the d-dimensional parabolic Anderson model driven by a Gaussian multiplicative noise, which is white in time and has a spatial covariance given by the Riesz kernel. The proof is based on the combination of Malliavin calculus techniques and the Stein's method for normal approximations.","PeriodicalId":50447,"journal":{"name":"Finance and Stochastics","volume":"1 1","pages":""},"PeriodicalIF":1.7,"publicationDate":"2022-05-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81454475","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}
引用次数: 0
A least-squares Monte Carlo approach to the estimation of enterprise risk 企业风险估计的最小二乘蒙特卡罗方法
IF 1.7 2区 经济学
Finance and Stochastics Pub Date : 2022-05-13 DOI: 10.1007/s00780-022-00478-7
Hongjun Ha, Daniel Bauer
{"title":"A least-squares Monte Carlo approach to the estimation of enterprise risk","authors":"Hongjun Ha, Daniel Bauer","doi":"10.1007/s00780-022-00478-7","DOIUrl":"https://doi.org/10.1007/s00780-022-00478-7","url":null,"abstract":"","PeriodicalId":50447,"journal":{"name":"Finance and Stochastics","volume":"26 1","pages":"417 - 459"},"PeriodicalIF":1.7,"publicationDate":"2022-05-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44268806","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}
引用次数: 2
Euler approximation and stability of the solution to stochastic differential equations with jumps under pathwise uniqueness 路径唯一性下具有跳跃的随机微分方程解的欧拉逼近与稳定性
IF 1.7 2区 经济学
Finance and Stochastics Pub Date : 2022-05-12 DOI: 10.1080/17442508.2022.2071107
Kaoutar Nasroallah, Y. Ouknine
{"title":"Euler approximation and stability of the solution to stochastic differential equations with jumps under pathwise uniqueness","authors":"Kaoutar Nasroallah, Y. Ouknine","doi":"10.1080/17442508.2022.2071107","DOIUrl":"https://doi.org/10.1080/17442508.2022.2071107","url":null,"abstract":"In this paper, we consider a stochastic differential equation with jumps for which pathwise uniqueness hold. We establish a fundamental mean square convergence theorem for the Euler approximation scheme. We provide some results on strong stability with respect to small perturbations of the initial conditions, and we study the convergence of Picard approximations.","PeriodicalId":50447,"journal":{"name":"Finance and Stochastics","volume":"77 1","pages":"266 - 302"},"PeriodicalIF":1.7,"publicationDate":"2022-05-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74267237","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}
引用次数: 2
Log-optimal and numéraire portfolios for market models stopped at a random time 市场模型的对数最优和numsamraire组合在随机时间停止
IF 1.7 2区 经济学
Finance and Stochastics Pub Date : 2022-05-06 DOI: 10.1007/s00780-022-00477-8
Tahir Choulli, Sina Yansori
{"title":"Log-optimal and numéraire portfolios for market models stopped at a random time","authors":"Tahir Choulli, Sina Yansori","doi":"10.1007/s00780-022-00477-8","DOIUrl":"https://doi.org/10.1007/s00780-022-00477-8","url":null,"abstract":"","PeriodicalId":50447,"journal":{"name":"Finance and Stochastics","volume":"26 1","pages":"535 - 585"},"PeriodicalIF":1.7,"publicationDate":"2022-05-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47966658","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}
引用次数: 4
Random periodic solutions for a class of hybrid stochastic differential equations 一类混合随机微分方程的随机周期解
IF 1.7 2区 经济学
Finance and Stochastics Pub Date : 2022-05-04 DOI: 10.1080/17442508.2022.2070019
Kenneth Uda
{"title":"Random periodic solutions for a class of hybrid stochastic differential equations","authors":"Kenneth Uda","doi":"10.1080/17442508.2022.2070019","DOIUrl":"https://doi.org/10.1080/17442508.2022.2070019","url":null,"abstract":"We present the existence and uniqueness of random periodic path for stochastic dynamical systems generated by random switching stochastic differential equations (SDEs). These classes of SDEs arise as concrete models in molecular dynamics, biochemistry, climatology, wireless communications, financial mathematics, biological and artificial neural networks, etc. Random periodic processes are inevitable in these classes of stochastic dynamical systems due to the nonlinearity of their processing and the presence of time-dependent applied current. In our investigation, we employed Lyapunov second method and the theory of M-matrices, which are verifiable in terms of the coefficients of the SDE and the switching rates.","PeriodicalId":50447,"journal":{"name":"Finance and Stochastics","volume":"1 1","pages":"211 - 234"},"PeriodicalIF":1.7,"publicationDate":"2022-05-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82392399","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}
引用次数: 2
Time-consistent consumption-portfolio control problems with regime-switching-modulated habit formation: an essentially cooperative approach 制度切换调制习惯形成的时间一致消费组合控制问题:一种本质上的合作方法
IF 1.7 2区 经济学
Finance and Stochastics Pub Date : 2022-05-04 DOI: 10.1080/17442508.2022.2070433
Yike Wang, Jingzhen Liu, Jiaqin Wei
{"title":"Time-consistent consumption-portfolio control problems with regime-switching-modulated habit formation: an essentially cooperative approach","authors":"Yike Wang, Jingzhen Liu, Jiaqin Wei","doi":"10.1080/17442508.2022.2070433","DOIUrl":"https://doi.org/10.1080/17442508.2022.2070433","url":null,"abstract":"This paper is devoted to consumption-portfolio control problems with regime-switching-modulated habit formation. The formation of a habit depends on the current regime, which leads to time inconsistency in optimal control. General utility functions are used to evaluate the preference for the consumption net of the habit. To derive an analytical solution, we consider an enlarged financial market with Markov jump assets. Then, the time-inconsistent problem for pre-commitment controls is reduced to solving a regime-switching Hamilton–Jacobi–Bellman (HJB) equation. In seeking a time-consistent control, we investigate an alternate problem by means of multi-person sequential games with an essentially cooperative approach. The analytical expression of the time-consistent control is derived via a straightforward application of the pre-commitment control results. Moreover, the limit case in which the mesh size of time approaches zero is studied.","PeriodicalId":50447,"journal":{"name":"Finance and Stochastics","volume":"62 1","pages":"235 - 265"},"PeriodicalIF":1.7,"publicationDate":"2022-05-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85764071","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}
引用次数: 0
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