ترغب بنشر مسار تعليمي؟ اضغط هنا

Backward stochastic Volterra integral equations with jumps in a general filtration

116   0   0.0 ( 0 )
 نشر من قبل Alexandre Popier
 تاريخ النشر 2020
  مجال البحث
والبحث باللغة English
 تأليف Alexandre Popier




اسأل ChatGPT حول البحث

In this paper, we study backward stochastic Volterra integral equations introduced in [26, 45] and extend the existence, uniqueness or comparison results for general filtration as in [31] (not only Brownian-Poisson setting). We also consider Lp-data and explore the time regularity of the solution in the It{^o} setting, which is also new in this jump setting.



قيم البحث

اقرأ أيضاً

We consider a class of Backward Stochastic Differential Equations with superlinear driver process $f$ adapted to a filtration supporting at least a $d$ dimensional Brownian motion and a Poisson random measure on ${mathbb R}^m- {0}.$ We consider the f ollowing class of terminal conditions $xi_1 = infty cdot 1_{{tau_1 le T}}$ where $tau_1$ is any stopping time with a bounded density in a neighborhood of $T$ and $xi_2 = infty cdot 1_{A_T}$ where $A_t$, $t in [0,T]$ is a decreasing sequence of events adapted to the filtration ${mathcal F}_t$ that is continuous in probability at $T$. A special case for $xi_2$ is $A_T = {tau_2 > T}$ where $tau_2$ is any stopping time such that $P(tau_2 =T) =0.$ In this setting we prove that the minimal supersolutions of the BSDE are in fact solutions, i.e., they attain almost surely their terminal values. We further show that the first exit time from a time varying domain of a $d$-dimensional diffusion process driven by the Brownian motion with strongly elliptic covariance matrix does have a continuous density; therefore such exit times can be used as $tau_1$ and $tau_2$ to define the terminal conditions $xi_1$ and $xi_2.$ The proof of existence of the density is based on the classical Greens functions for the associated PDE.
This paper introduces the notion of a filtration-consistent dynamic operator with a floor, by suitably formulating four axioms. It is shown that under some suitable conditions, a filtration-consistent dynamic operator with a continuous upper-bounded floor is necessarily represented by the solution of a backward stochastic differential equation reflected upwards on the floor.
By analogy with the theory of Backward Stochastic Differential Equations, we define Backward Stochastic Difference Equations on spaces related to discrete time, finite state processes. This paper considers these processes as constructions in their ow n right, not as approximations to the continuous case. We establish the existence and uniqueness of solutions under weaker assumptions than are needed in the continuous time setting, and also establish a comparison theorem for these solutions. The conditions of this theorem are shown to approximate those required in the continuous time setting. We also explore the relationship between the driver $F$ and the set of solutions; in particular, we determine under what conditions the driver is uniquely determined by the solution. Applications to the theory of nonlinear expectations are explored, including a representation result.
464 - Shige Peng , Zhe Yang 2009
In this paper we discuss new types of differential equations which we call anticipated backward stochastic differential equations (anticipated BSDEs). In these equations the generator includes not only the values of solutions of the present but also the future. We show that these anticipated BSDEs have unique solutions, a comparison theorem for their solutions, and a duality between them and stochastic differential delay equations.
We consider ergodic backward stochastic differential equations in a discrete time setting, where noise is generated by a finite state Markov chain. We show existence and uniqueness of solutions, along with a comparison theorem. To obtain this result, we use a Nummelin splitting argument to obtain ergodicity estimates for a discrete time Markov chain which hold uniformly under suitable perturbations of its transition matrix. We conclude with an application of this theory to a treatment of an ergodic control problem.
التعليقات
جاري جلب التعليقات جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
mircosoft-partner

هل ترغب بارسال اشعارات عن اخر التحديثات في شمرا-اكاديميا