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RBDSDEs with jumps and optional Barrier and mean field game with common noise RBDSDEs与跳跃和可选的障碍和平均场游戏与常见的噪音
IF 1.7 2区 经济学
Finance and Stochastics Pub Date : 2022-08-30 DOI: 10.1080/17442508.2022.2113080
Badr-eddine Berrhazi, M. El Fatini, A. Hilbert, N. Mrhardy, R. Pettersson
{"title":"RBDSDEs with jumps and optional Barrier and mean field game with common noise","authors":"Badr-eddine Berrhazi, M. El Fatini, A. Hilbert, N. Mrhardy, R. Pettersson","doi":"10.1080/17442508.2022.2113080","DOIUrl":"https://doi.org/10.1080/17442508.2022.2113080","url":null,"abstract":"ABSTRACT In this paper, we study a generalization of reflected backward doubly stochastic differential equations (RBDSDEs) and present a link to a general mean field game. In our case, the RBDSDEs are associated with a lower optional not right continuous barrier. First, we establish the existence and uniqueness of a solution of such RBDSDEs. We then study a mean field game with a new type of common noise related to an electricity grid with storage allowing jumps and prove the existence of a mean field Nash equilibrium.","PeriodicalId":50447,"journal":{"name":"Finance and Stochastics","volume":"166 1","pages":"615 - 634"},"PeriodicalIF":1.7,"publicationDate":"2022-08-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80466489","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
Continuity and approximation properties of solutions to fractional neutral stochastic functional differential equations with non-Lipschitz coefficients 非lipschitz系数分数中立型随机泛函微分方程解的连续性和逼近性
IF 1.7 2区 经济学
Finance and Stochastics Pub Date : 2022-08-30 DOI: 10.1080/17442508.2022.2114801
Jiaping Wen, P. He, Wujun Lv
{"title":"Continuity and approximation properties of solutions to fractional neutral stochastic functional differential equations with non-Lipschitz coefficients","authors":"Jiaping Wen, P. He, Wujun Lv","doi":"10.1080/17442508.2022.2114801","DOIUrl":"https://doi.org/10.1080/17442508.2022.2114801","url":null,"abstract":"ABSTRACT This paper aims to investigate a fractional neutral stochastic functional differential equation (FNSFDE) with non-Lipschitz coefficients. Under the assumptions, we first establish the continuity of the solution in the fractional order of the equation. Furthermore, an Euler-Maruyama (EM) approximation is constructed and then we obtain the strong convergence of the numerical scheme. Specially, if the non-Lipschitz conditions are replaced with the Lipschitz conditions, we shall get a definite convergence rate, which is related to the fractional order of the equation. Finally, we consider the averaging principle for the fractional neutral stochastic equation, which provides us with an easy way to study the properties of the equation.","PeriodicalId":50447,"journal":{"name":"Finance and Stochastics","volume":"4 1","pages":"662 - 695"},"PeriodicalIF":1.7,"publicationDate":"2022-08-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76839459","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
Approximate controllability of semi-linear stochastic integrodifferential system with multiple delays and Poisson jumps in control 具有多时滞和泊松跳的半线性随机积分微分系统的近似可控性
IF 1.7 2区 经济学
Finance and Stochastics Pub Date : 2022-07-31 DOI: 10.1080/17442508.2022.2105145
A. Annamalai, Ravikumar Kasinathan, Ramkumar Kasinathan
{"title":"Approximate controllability of semi-linear stochastic integrodifferential system with multiple delays and Poisson jumps in control","authors":"A. Annamalai, Ravikumar Kasinathan, Ramkumar Kasinathan","doi":"10.1080/17442508.2022.2105145","DOIUrl":"https://doi.org/10.1080/17442508.2022.2105145","url":null,"abstract":"The objective of this paper is to interpret the approximate controllability of a semi-linear stochastic integrodifferential system with multiple delays and Poisson jumps in control in infinite-dimensional spaces. Sufficient conditions for the approximate controllability of semi-linear control system have been established. The results are obtained using the Banach fixed point theorem and the theory of resolvent operator developed in Grimmer [Resolvent operator for integral equations in Banach spaces, Trans. Am. Math. Soc. 273 (1982), pp. 333– 349.]. An example is introduced to show the effectiveness of the result.","PeriodicalId":50447,"journal":{"name":"Finance and Stochastics","volume":"57 1","pages":"465 - 482"},"PeriodicalIF":1.7,"publicationDate":"2022-07-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85626293","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
Strong convergence rate of the averaging principle for a class of slow–fast stochastic evolution equations 一类慢-快随机演化方程平均原理的强收敛速率
IF 1.7 2区 经济学
Finance and Stochastics Pub Date : 2022-07-01 DOI: 10.1080/17442508.2022.2093112
Jie Xu, Qiqi Lian, Jicheng Liu
{"title":"Strong convergence rate of the averaging principle for a class of slow–fast stochastic evolution equations","authors":"Jie Xu, Qiqi Lian, Jicheng Liu","doi":"10.1080/17442508.2022.2093112","DOIUrl":"https://doi.org/10.1080/17442508.2022.2093112","url":null,"abstract":"ABSTRACT We prove a strong convergence rate of the averaging principle for general two-time-scales stochastic evolution equations driven by cylindrical Wiener processes. In particular, our general result can be used to deal with a large class of quasi-linear stochastic partial differential equations, such as stochastic reaction–diffusion equations, stochastic p-Laplace equations, stochastic porous media equations, and so on.","PeriodicalId":50447,"journal":{"name":"Finance and Stochastics","volume":"9 1","pages":"581 - 614"},"PeriodicalIF":1.7,"publicationDate":"2022-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77555992","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
Weak solution of a stochastic 3D nonlocal Cahn–Hilliard–Navier–Stokes systems with shear-dependent viscosity 具有剪切依赖黏度的三维随机非局部Cahn-Hilliard-Navier-Stokes系统的弱解
IF 1.7 2区 经济学
Finance and Stochastics Pub Date : 2022-06-29 DOI: 10.1080/17442508.2022.2092403
A. Ndongmo Ngana, G. Deugoue, T. Tachim Medjo
{"title":"Weak solution of a stochastic 3D nonlocal Cahn–Hilliard–Navier–Stokes systems with shear-dependent viscosity","authors":"A. Ndongmo Ngana, G. Deugoue, T. Tachim Medjo","doi":"10.1080/17442508.2022.2092403","DOIUrl":"https://doi.org/10.1080/17442508.2022.2092403","url":null,"abstract":"ABSTRACT We consider the stochastic nonlocal Cahn–Hilliard–Navier–Stokes system with shear-dependent viscosity on a bounded domain , d = 2, 3, driven by a multiplicative noise of Lévy and Gaussian types. The velocity u is governed by a Navier–Stokes system with a shear-dependent viscosity controlled by a power p>2. This system is nonlinearly coupled through the Korteweg force with a convective nonlocal Cahn–Hilliard equation for the order parameter φ. The existence of a global weak martingale solution is proved. In the 2D case, we prove the pathwise uniqueness of the weak solution, when .","PeriodicalId":50447,"journal":{"name":"Finance and Stochastics","volume":"214 1","pages":"521 - 580"},"PeriodicalIF":1.7,"publicationDate":"2022-06-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"72833080","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 class of short-term models for the oil industry that accounts for speculative oil storage 石油工业的一类短期模型，用于解释投机性石油储存
IF 1.7 2区 经济学
Finance and Stochastics Pub Date : 2022-06-28 DOI: 10.1007/s00780-022-00481-y
Y. Achdou, Charles Bertucci, J. Lasry, P. Lions, A. Rostand, J. Scheinkman
{"title":"A class of short-term models for the oil industry that accounts for speculative oil storage","authors":"Y. Achdou, Charles Bertucci, J. Lasry, P. Lions, A. Rostand, J. Scheinkman","doi":"10.1007/s00780-022-00481-y","DOIUrl":"https://doi.org/10.1007/s00780-022-00481-y","url":null,"abstract":"","PeriodicalId":50447,"journal":{"name":"Finance and Stochastics","volume":"26 1","pages":"631 - 669"},"PeriodicalIF":1.7,"publicationDate":"2022-06-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"52093911","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
On the role of skewness and kurtosis in tempered stable (CGMY) Lévy models in finance 偏度和峰度在调和稳定(CGMY)金融模型中的作用
IF 1.7 2区 经济学
Finance and Stochastics Pub Date : 2022-06-28 DOI: 10.1007/s00780-022-00482-x
S. Asmussen
{"title":"On the role of skewness and kurtosis in tempered stable (CGMY) Lévy models in finance","authors":"S. Asmussen","doi":"10.1007/s00780-022-00482-x","DOIUrl":"https://doi.org/10.1007/s00780-022-00482-x","url":null,"abstract":"","PeriodicalId":50447,"journal":{"name":"Finance and Stochastics","volume":"26 1","pages":"383 - 416"},"PeriodicalIF":1.7,"publicationDate":"2022-06-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44643523","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
Adaptive importance sampling for multilevel Monte Carlo Euler method 多层蒙特卡罗欧拉法的自适应重要抽样
IF 1.7 2区 经济学
Finance and Stochastics Pub Date : 2022-06-25 DOI: 10.1080/17442508.2022.2084338
M. Ben Alaya, Kaouther Hajji, Ahmed Kebaier
{"title":"Adaptive importance sampling for multilevel Monte Carlo Euler method","authors":"M. Ben Alaya, Kaouther Hajji, Ahmed Kebaier","doi":"10.1080/17442508.2022.2084338","DOIUrl":"https://doi.org/10.1080/17442508.2022.2084338","url":null,"abstract":"This paper focuses on the study of an original combination of the Multilevel Monte Carlo method introduced by Giles [Multilevel Monte Carlo path simulation, Oper. Res. 56(3) (2008), pp. 607–617.] and the popular importance sampling technique. To compute the optimal choice of the parameter involved in the importance sampling method, we rely on Robbins–Monro type stochastic algorithms. On the one hand, we extend our previous work [M. Ben Alaya, K. Hajji and A. Kebaier, Importance sampling and statistical Romberg method, Bernoulli 21(4) (2015), pp. 1947–1983.] to the Multilevel Monte Carlo setting. On the other hand, we improve [M. Ben Alaya, K. Hajji and A. Kebaier, Importance sampling and statistical Romberg method, Bernoulli 21(4) (2015), pp. 1947–1983.] by providing a new adaptive algorithm avoiding the discretization of any additional process. Furthermore, from a technical point of view, the use of the same stochastic algorithms as in [M. Ben Alaya, K. Hajji and A. Kebaier, Importance sampling and statistical Romberg method, Bernoulli 21(4) (2015), pp. 1947–1983.] appears to be problematic. To overcome this issue, we employ an alternative version of stochastic algorithms with projection (see, e.g. Laruelle, Lehalle and Pagès [Optimal posting price of limit orders: learning by trading, Math. Financ. Econ. 7(3) (2013), pp. 359–403.]). In this setting, we show innovative limit theorems for a doubly indexed stochastic algorithm which appear to be crucial to study the asymptotic behaviour of the new adaptive Multilevel Monte Carlo estimator. Finally, we illustrate the efficiency of our method through applications from quantitative finance.","PeriodicalId":50447,"journal":{"name":"Finance and Stochastics","volume":"52 1","pages":"303 - 327"},"PeriodicalIF":1.7,"publicationDate":"2022-06-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89088176","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: 6
Optimal dividends under a drawdown constraint and a curious square-root rule 在收缩约束和一个奇怪的平方根法则下的最优股息
IF 1.7 2区 经济学
Finance and Stochastics Pub Date : 2022-06-24 DOI: 10.1007/s00780-023-00500-6
H. Albrecher, P. Azcue, N. Muler
{"title":"Optimal dividends under a drawdown constraint and a curious square-root rule","authors":"H. Albrecher, P. Azcue, N. Muler","doi":"10.1007/s00780-023-00500-6","DOIUrl":"https://doi.org/10.1007/s00780-023-00500-6","url":null,"abstract":"","PeriodicalId":50447,"journal":{"name":"Finance and Stochastics","volume":"27 1","pages":"341 - 400"},"PeriodicalIF":1.7,"publicationDate":"2022-06-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"52094111","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
Two generalizations of Mehler's formula in white noise analysis 白噪声分析中梅勒公式的两个推广
IF 1.7 2区 经济学
Finance and Stochastics Pub Date : 2022-06-21 DOI: 10.1080/17442508.2022.2089039
W. Bock, Maximilian Bock
{"title":"Two generalizations of Mehler's formula in white noise analysis","authors":"W. Bock, Maximilian Bock","doi":"10.1080/17442508.2022.2089039","DOIUrl":"https://doi.org/10.1080/17442508.2022.2089039","url":null,"abstract":"ABSTRACT Mehler's formula is an important tool in Gaussian analysis. In this article, we study two generalizations of Mehler's formula for the Ornstein–Uhlenbeck semigroup, i.e. the semigroup generated by the number operator. The first generalization leads to transformation groups which have as infinitesimal generator a perturbation of the number operator with suitable integral kernel operators, which are well studied in white noise analysis. For the second one, we characterize the complex Hida measures for which a version of Mehler's formula for the Ornstein–Uhlenbeck semigroup can be extended to. We apply this result to the Feynman integrand for a quadratic potential. Here the time independent eigenstates of the considered transformation groups and the time evolution of eigenvalues are provided.","PeriodicalId":50447,"journal":{"name":"Finance and Stochastics","volume":"299 1","pages":"501 - 520"},"PeriodicalIF":1.7,"publicationDate":"2022-06-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79655850","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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