共查询到20条相似文献,搜索用时 828 毫秒
1.
Thibaut Mastrolia 《Stochastic Processes and their Applications》2018,128(3):897-938
In this paper, we provide conditions which ensure that stochastic Lipschitz BSDEs admit Malliavin differentiable solutions. We investigate the problem of existence of densities for the first components of solutions to general path-dependent stochastic Lipschitz BSDEs and obtain results for the second components in particular cases. We apply these results to both the study of a gene expression model in biology and to the classical pricing problems in mathematical finance. 相似文献
2.
Juliang Yin 《Bulletin des Sciences Mathématiques》2010,134(8):799-815
This paper investigates a class of multi-dimensional stochastic differential equations with one reflecting lower barrier (RBSDEs in short), where the random obstacle is described as an Itô diffusion type of stochastic differential equation. The existence and uniqueness results for adapted solutions to such RBSDEs are established based on a penalization scheme and some higher moment estimates for solutions to penalized BSDEs under the Lipschitz condition and a higher moment condition on the coefficients. Finally, two examples are given to illustrate our theory and their applications. 相似文献
3.
ABSTRACTThis paper introduces a class of backward stochastic differential equations (BSDEs), whose coefficients not only depend on the value of its solutions of the present but also the past and the future. For a sufficiently small time delay or a sufficiently small Lipschitz constant, the existence and uniqueness of such BSDEs is obtained. As an adjoint process, a class of stochastic differential equations (SDEs) is introduced, whose coefficients also depend on the present, the past and the future of its solutions. The existence and uniqueness of such SDEs is proved for a sufficiently small time advance or a sufficiently small Lipschitz constant. A duality between such BSDEs and SDEs is established. 相似文献
4.
《Stochastic Processes and their Applications》2019,129(11):4597-4637
In this paper, we prove new convergence results improving the ones by Chassagneux et al. (2012) for the discrete-time approximation of multidimensional obliquely reflected BSDEs. These BSDEs, arising in the study of switching problems, were considered by Hu and Tang (2010) and generalized by Hamadène and Zhang (2010) and Chassagneux et al. (2011). Our main result is a rate of convergence obtained in the Lipschitz setting and under the same structural conditions on the generator as the one required for the existence and uniqueness of a solution to the obliquely reflected BSDE. 相似文献
5.
贾广岩 《数学年刊A辑(中文版)》2007,(5)
考虑一类一维倒向随机微分方程(BSDE),其系数关于y满足左Lipschitz条件(可能是不连续的),关于z满足Lipschitz条件.在这样的条件下,证明了BSDE的解是存在的,并且得到了相应的比较定理. 相似文献
6.
This paper is devoted to the $L^p$ ($p>1$) solutions of
one-dimensional backward stochastic differential equations (BSDEs
for short) with general time intervals and generators satisfying
some non-uniform conditions in $t$ and $\omega$. An existence and
uniqueness result, a comparison theorem and an existence result for
the minimal solutions are respectively obtained, which considerably
improve some known works. Some classical techniques used to deal
with the existence and uniqueness of $L^p$ ($p>1$) solutions of
BSDEs with Lipschitz or linear-growth generators are also developed
in this paper. 相似文献
7.
8.
We consider backward stochastic differential equations (BSDEs) related to a finite continuous time single jump process. We prove the existence and uniqueness of solutions when the coefficients satisfy Lipschitz continuity conditions. A comparison theorem for these solutions is also given. Applications to the theory of nonlinear expectations are then investigated. 相似文献
9.
Sheng Jun Fan 《数学学报(英文版)》2009,25(10):1681-1692
Under the Lipschitz assumption and square integrable assumption on g, Jiang proved that Jensen's inequality for BSDEs with generator g holds in general if and only if g is independent of y, g is super homogenous in z and g(t, 0) = 0, a.s., a.e.. In this paper, based on Jiang's results, under the same assumptions as Jiang's, we investigate the necessary and sufficient condition on g under which Jensen's inequality for BSDEs with generator g holds for some specific convex functions, which generalizes some known results on Jensen's inequality for BSDEs. 相似文献
10.
This paper is interested in solving a multidimensional backward stochastic differential equation (BSDE) whose generator satisfies the Osgood condition in y and the Lipschitz condition in z. We establish an existence and uniqueness result of solutions for this kind of BSDEs, which generalizes some known results. 相似文献
11.
Sheng-jun Fan 《应用数学学报(英文版)》2009,25(1):11-20
Under the Lipschitz and square integrable assumptions on the generator g of BSDEs, this paper proves that if g is positively homogeneous in (y, z) and is decreasing in y, then the Moment inequality for BSDEs with generator g holds in general, and if g is positively homogeneous and sub-additive in (y, z), then the HSlder inequality and Minkowski inequality for BSDEs with generator g hold in general. 相似文献
12.
13.
This paper is devoted to real valued backward stochastic differential equations (BSDEs for short) with generators which satisfy a stochastic Lipschitz condition involving BMO martingales. This framework arises naturally when looking at the BSDE satisfied by the gradient of the solution to a BSDE with quadratic growth in Z. We first prove an existence and uniqueness result from which we deduce the differentiability with respect to parameters of solutions to quadratic BSDEs. Finally, we apply these results to prove the existence and uniqueness of a mild solution to a parabolic partial differential equation in Hilbert space with nonlinearity having quadratic growth in the gradient of the solution. 相似文献
14.
在生成元g满足关于y单调且关于z Lipschitz连续的条件下,范(2007)得到了倒向随机微分方程L~p解对终值的单调连续结果.在g关于y单调且关于z一致连续的条件下证明了倒向随机微分方程L~p解的单调连续性,推广了范(2007)的工作,并且方法是新的. 相似文献
15.
Samuel N. Cohen 《Stochastic Processes and their Applications》2012,122(4):1601-1626
We consider filtration consistent nonlinear expectations in probability spaces satisfying only the usual conditions and separability. Under a domination assumption, we demonstrate that these nonlinear expectations can be expressed as the solutions to Backward Stochastic Differential Equations with Lipschitz continuous drivers, where both the martingale and the driver terms are permitted to jump, and the martingale representation is infinite dimensional. To establish this result, we show that this domination condition is sufficient to guarantee that the comparison theorem for BSDEs will hold, and we generalise the nonlinear Doob–Meyer decomposition of Peng to a general context. 相似文献
16.
This paper provides a simple approach for the consideration of quadratic BSDEs with bounded terminal conditions. Using solely probabilistic arguments, we retrieve the existence and uniqueness result derived via PDE-based methods by Kobylanski (2000) [14]. This approach is related to the study of quadratic BSDEs presented by Tevzadze (2008) [19]. Our argumentation, as in Tevzadze (2008) [19], highly relies on the theory of BMO martingales which was used for the first time for BSDEs by Hu et al. (2005) [12]. However, we avoid in our method any fixed point argument and use Malliavin calculus to overcome the difficulty. Our new scheme of proof allows also to extend the class of quadratic BSDEs, for which there exists a unique solution: we incorporate delayed quadratic BSDEs, whose driver depends on the recent past of the Y component of the solution. When the delay vanishes, we verify that the solution of a delayed quadratic BSDE converges to the solution of the corresponding classical non-delayed quadratic BSDE. 相似文献
17.
In this paper we study the path regularity of the adpated solutions to a class of backward stochastic differential equations
(BSDE, for short) whose terminal values are allowed to be functionals of a forward diffusion. Using the new representation
formula for the adapted solutions established in our previous work [7], we are able to show, under the mimimum Lipschitz conditions
on the coefficients, that for a fairly large class of BSDEs whose terminal values are functionals that are either Lipschitz
under the L
∞
-norm or under the L
1
-norm, then there exists a version of the adapted solution pair that has at least càdlàg paths. In particular, in the latter
case the version can be chosen so that the paths are in fact continuous.
Received: 26 May 2000 / Revised version: 1 December 2000 / Published online: 19 December 2001 相似文献
18.
A class of stochastic differential equations with super-linear growth and non-Lipschitz coefficients
The purpose of this paper is to study some properties of solutions to one-dimensional as well as multidimensional stochastic differential equations (SDEs in short) with super-linear growth and non-Lipschitz conditions on the coefficients. Taking inspiration from [K. Bahlali, E.H. Essaky, M. Hassani, and E. Pardoux Existence, uniqueness and stability of backward stochastic differential equation with locally monotone coefficient, C.R.A.S. Paris. 335(9) (2002), pp. 757–762; K. Bahlali, E. H. Essaky, and H. Hassani, Multidimensional BSDEs with super-linear growth coefficients: Application to degenerate systems of semilinear PDEs, C. R. Acad. Sci. Paris, Ser. I. 348 (2010), pp. 677-682; K. Bahlali, E. H. Essaky, and H. Hassani, p-Integrable solutions to multidimensional BSDEs and degenerate systems of PDEs with logarithmic nonlinearities, (2010). Available at arXiv:1007.2388v1 [math.PR]], we introduce a new local condition which ensures the pathwise uniqueness, as well as the non-contact property. We moreover show that the solution produces a stochastic flow of continuous maps and satisfies a large deviations principle of Freidlin–Wentzell type. Our conditions on the coefficients go beyond the existing ones in the literature. For instance, the coefficients are not assumed uniformly continuous and therefore cannot satisfy the classical Osgood condition. The drift coefficient could not be locally monotone and the diffusion is neither locally Lipschitz nor uniformly elliptic. Our conditions on the coefficients are, in some sense, near the best possible. Our results are sharp and mainly based on Gronwall lemma and the localization of the time parameter in concatenated intervals. 相似文献
19.
In a recent paper, Soner, Touzi and Zhang (2012) [19] have introduced a notion of second order backward stochastic differential equations (2BSDEs), which are naturally linked to a class of fully non-linear PDEs. They proved existence and uniqueness for a generator which is uniformly Lipschitz in the variables y and z. The aim of this paper is to extend these results to the case of a generator satisfying a monotonicity condition in y. More precisely, we prove existence and uniqueness for 2BSDEs with a generator which is Lipschitz in z and uniformly continuous with linear growth in y. Moreover, we emphasize throughout the paper the major difficulties and differences due to the 2BSDE framework. 相似文献
20.
Guangyan Jia 《Comptes Rendus Mathematique》2006,342(9):685-688
In this Note, we deal with one-dimensional backward stochastic differential equations (BSDEs) where the coefficient is left-Lipschitz in y (may be discontinuous) and Lipschitz in z, but without explicit growth constraint. We prove, in this setting, an existence theorem for backward stochastic differential equations. To cite this article: G. Jia, C. R. Acad. Sci. Paris, Ser. I 342 (2006). 相似文献