Pub Date : 2022-08-30DOI: 10.1080/17442508.2022.2113080
Badr-eddine Berrhazi, M. El Fatini, A. Hilbert, N. Mrhardy, R. Pettersson
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.
{"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}
Pub Date : 2022-08-30DOI: 10.1080/17442508.2022.2114801
Jiaping Wen, P. He, Wujun Lv
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.
{"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}
Pub Date : 2022-07-31DOI: 10.1080/17442508.2022.2105145
A. Annamalai, Ravikumar Kasinathan, Ramkumar Kasinathan
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.
{"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}
Pub Date : 2022-07-01DOI: 10.1080/17442508.2022.2093112
Jie Xu, Qiqi Lian, Jicheng Liu
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.
{"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}
Pub Date : 2022-06-29DOI: 10.1080/17442508.2022.2092403
A. Ndongmo Ngana, G. Deugoue, T. Tachim Medjo
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 .
{"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}
Pub Date : 2022-06-28DOI: 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}
Pub Date : 2022-06-28DOI: 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}
Pub Date : 2022-06-25DOI: 10.1080/17442508.2022.2084338
M. Ben Alaya, Kaouther Hajji, Ahmed Kebaier
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.
本文重点研究了Giles [multi - level Monte Carlo path simulation, Oper]提出的一种原始组合的多电平蒙特卡罗方法。Res. 56(3) (2008)， pp. 607-617。]和流行的重要性抽样技术。为了计算重要性抽样方法中涉及的参数的最优选择，我们依靠罗宾斯-门罗型随机算法。一方面，我们扩展了以前的工作。Ben Alaya, K. Hajji和A. Kebaier，重要性抽样和统计Romberg方法，Bernoulli 21(4) (2015)， pp. 1947-1983。到多层蒙特卡洛设置。另一方面，我们改进了[M]。Ben Alaya, K. Hajji和A. Kebaier，重要性抽样和统计Romberg方法，Bernoulli 21(4) (2015)， pp. 1947-1983。通过提供一种新的自适应算法来避免任何额外过程的离散化。此外，从技术角度来看，使用与[M]中相同的随机算法。Ben Alaya, K. Hajji和A. Kebaier，重要性抽样和统计Romberg方法，Bernoulli 21(4) (2015)， pp. 1947-1983。似乎有问题。为了克服这个问题，我们采用了带有投影的随机算法的替代版本(参见，例如Laruelle, Lehalle和pag[限价单的最优发布价格:通过交易学习，数学])。Financ。经济学，7(3)(2013)，pp. 359-403。在这种情况下，我们展示了双索引随机算法的创新极限定理，这对于研究新的自适应多电平蒙特卡罗估计器的渐近行为至关重要。最后，我们通过量化金融的应用来说明我们方法的有效性。
{"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}
Pub Date : 2022-06-24DOI: 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}
Pub Date : 2022-06-21DOI: 10.1080/17442508.2022.2089039
W. Bock, Maximilian Bock
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.
{"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}
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