This paper considers a mean-field type stochastic control problem where the dynamics is governed by a forward and backward stochastic differential equation (SDE) driven by Lévy processes and the information avail...This paper considers a mean-field type stochastic control problem where the dynamics is governed by a forward and backward stochastic differential equation (SDE) driven by Lévy processes and the information available to the controller is possibly less than the overall information. All the system coefficients and the objective performance functional are allowed to be random, possibly non-Markovian. Malliavin calculus is employed to derive a maximum principle for the optimal control of such a system where the adjoint process is explicitly expressed.展开更多
In this paper we elaborate a general expression of the conditional expectation related to pricing problem of the American options using the Malliavin derivative （without localization）. This work is a generalization ...In this paper we elaborate a general expression of the conditional expectation related to pricing problem of the American options using the Malliavin derivative （without localization）. This work is a generalization of paper of Bally et al. （2005） [ 1 ] for the one dimensional case. Basing on the density function of the asset price, Bally and al. used the Malliavin calculus to evaluate the conditional expectation related to pricing American option problem, but in our work we use the Malliavin derivative to resolve the previous problem.展开更多
Let B^H1,K1 and BH2,K2 be two independent bi-fractional Brownian motions. In this paper, as a natural extension to the fractional regression model, we consider the asymptotic behavior of the sequence Sn：=∑i=0^n-1K...Let B^H1,K1 and BH2,K2 be two independent bi-fractional Brownian motions. In this paper, as a natural extension to the fractional regression model, we consider the asymptotic behavior of the sequence Sn：=∑i=0^n-1K（n^αBi^H,K1）（Bi＋1^H2,K2-Bi^H2,K2）where K is a standard Gaussian kernel function and the bandwidth parameter α satisfies certain hypotheses. We show that its limiting distribution is a mixed normal law involving the local time of the bi-fractional Brownian motion B^H1,K1. We also give the stable convergence of the sequence Sn by using the techniques of the Malliavin calculus.展开更多
In this paper we study the infinite dimensional Malliavin calculus, and apply it to determingwhen the solution of an infinite dimensional stochastic differential equation has the property thatits finite dimensional di...In this paper we study the infinite dimensional Malliavin calculus, and apply it to determingwhen the solution of an infinite dimensional stochastic differential equation has the property thatits finite dimensional distributions possess smooth density.展开更多
In this paper, we apply Malliavin calculus to discuss when the solutions of stochastic differen-tial equations (SDE's) with time-dependent coefficients have smooth density. Under Hormander'scondition,we conclu...In this paper, we apply Malliavin calculus to discuss when the solutions of stochastic differen-tial equations (SDE's) with time-dependent coefficients have smooth density. Under Hormander'scondition,we conclude that the solutions of the SDE's have smooth density. As a consequence,we get the hypoellipticity for inhomogeneous differential operators.展开更多
Let u(t,x)be the solution to the one-dimensional nonlinear stochastic heat equation driven by space-time white noise with u(0,x)=1 for all x∈R.In this paper,we prove the law of the iterated logarithm(LIL for short)an...Let u(t,x)be the solution to the one-dimensional nonlinear stochastic heat equation driven by space-time white noise with u(0,x)=1 for all x∈R.In this paper,we prove the law of the iterated logarithm(LIL for short)and the functional LIL for a linear additive functional of the form∫[0,R]u(t,x)dx and the nonlinear additive functionals of the form∫[0,R]g(u(t,x))dx,where g:R→R is nonrandom and Lipschitz continuous,as R→∞for fixed t>0,using the localization argument.展开更多
文摘This paper considers a mean-field type stochastic control problem where the dynamics is governed by a forward and backward stochastic differential equation (SDE) driven by Lévy processes and the information available to the controller is possibly less than the overall information. All the system coefficients and the objective performance functional are allowed to be random, possibly non-Markovian. Malliavin calculus is employed to derive a maximum principle for the optimal control of such a system where the adjoint process is explicitly expressed.
文摘In this paper we elaborate a general expression of the conditional expectation related to pricing problem of the American options using the Malliavin derivative （without localization）. This work is a generalization of paper of Bally et al. （2005） [ 1 ] for the one dimensional case. Basing on the density function of the asset price, Bally and al. used the Malliavin calculus to evaluate the conditional expectation related to pricing American option problem, but in our work we use the Malliavin derivative to resolve the previous problem.
基金Acknowledgements The authors would like to thank the anonymous referees whose remarks and suggestions greatly improved the presentation of the paper. Guangjun Shen was supported in part by the National Natural Science Foundation of China （Grant No. 11271020） and the Natural Science Foundation of Anhui Province （1208085MA11）. Litan YAN was partially supported by the National Natural Science Foundation of China （Grant No. 11171062） and the Innovation Program of Shanghai Municipal Education Commission （12ZZ063）.
文摘Let B^H1,K1 and BH2,K2 be two independent bi-fractional Brownian motions. In this paper, as a natural extension to the fractional regression model, we consider the asymptotic behavior of the sequence Sn：=∑i=0^n-1K（n^αBi^H,K1）（Bi＋1^H2,K2-Bi^H2,K2）where K is a standard Gaussian kernel function and the bandwidth parameter α satisfies certain hypotheses. We show that its limiting distribution is a mixed normal law involving the local time of the bi-fractional Brownian motion B^H1,K1. We also give the stable convergence of the sequence Sn by using the techniques of the Malliavin calculus.
基金This project is supported by the National Natural Science Foundation of China
文摘In this paper we study the infinite dimensional Malliavin calculus, and apply it to determingwhen the solution of an infinite dimensional stochastic differential equation has the property thatits finite dimensional distributions possess smooth density.
基金The project supported by National Natural Science Foundation of China Crant 18971061
文摘In this paper, we apply Malliavin calculus to discuss when the solutions of stochastic differen-tial equations (SDE's) with time-dependent coefficients have smooth density. Under Hormander'scondition,we conclude that the solutions of the SDE's have smooth density. As a consequence,we get the hypoellipticity for inhomogeneous differential operators.
基金supported by the National Natural Science Foundation of China(11771178 and 12171198)the Science and Technology Development Program of Jilin Province(20210101467JC)+1 种基金the Science and Technology Program of Jilin Educational Department during the“13th Five-Year”Plan Period(JJKH20200951KJ)the Fundamental Research Funds for the Central Universities。
文摘Let u(t,x)be the solution to the one-dimensional nonlinear stochastic heat equation driven by space-time white noise with u(0,x)=1 for all x∈R.In this paper,we prove the law of the iterated logarithm(LIL for short)and the functional LIL for a linear additive functional of the form∫[0,R]u(t,x)dx and the nonlinear additive functionals of the form∫[0,R]g(u(t,x))dx,where g:R→R is nonrandom and Lipschitz continuous,as R→∞for fixed t>0,using the localization argument.
基金supported by the National Natural Science Foundation of China(Grant No.11401313)the Natural Science Foundation of Jiangsu Province(Grant No.BK20161579)+3 种基金the China Postdoctoral Science Foundation(Grant Nos.2014M5603682015T80475)2014 Qing Lan Project,Financial Engineering Key Laboratory of Jiangsu Province(Grant No.NSK201504)PAPD
