相关论文: Dual Representation of Minimal Supersolutions of C…
We study the existence of minimal supersolutions of BSDEs under a family of mutually singular probability measures. We consider generators that are jointly lower semicontinuous, positive, and either convex in the control variable and…
We study supersolutions of a backward stochastic differential equation, the control processes of which are constrained to be continuous semimartingales of the form $dZ = {\Delta}dt + {\Gamma}dW$. The generator may depend on the…
We study the nonlinear operator of mapping the terminal value $\xi$ to the corresponding minimal supersolution of a backward stochastic differential equation with the generator being monotone in $y$, convex in $z$, jointly lower…
We consider multidimensional quadratic BSDEs with bounded and unbounded terminal conditions. We provide sufficient conditions which guarantee existence and uniqueness of solutions. In particular, these conditions are satisfied if the…
We study the existence and uniqueness of minimal supersolutions of backward stochastic differential equations with generators that are jointly lower semicontinuous, bounded below by an affine function of the control variable and satisfy a…
We consider multidimensional quadratic BSDEs with bounded and unbounded terminal conditions. We provide sufficient conditions which guarantee existence and uniqueness of solutions. In particular, these conditions are satisfied if the…
We study the existence of a minimal supersolution for backward stochastic differential equations when the terminal data can take the value +$\infty$ with positive probability. We deal with equations on a general filtered probability space…
We introduce the notion of mild supersolution for an obstacle problem in an infinite dimensional Hilbert space. The minimal supersolution of this problem is given in terms of a reflected BSDEs in an infinite dimensional Markovian framework.…
In this paper we provide conditions for the existence of supersolutions to BSDEs with mean-reflections on the $Z$ component. We show that, contrary to BSDEs with mean-reflections on the $Y$ component, we cannot expect a supersolution with a…
The dynamic concave utility (or the dynamic convex risk measure) of an unbounded endowment is studied and represented as the value process in the unique solution of a backward stochastic differential equation (BSDE) with an unbounded…
We consider backward stochastic differential equations (BSDE) with nonlinear generators typically of quadratic growth in the control variable. A measure solution of such a BSDE will be understood as a probability measure under which the…
In this paper, we prove that a kind of second order stochastic differential operator can be represented by the limit of solutions of BSDEs with uniformly continuous coefficients. This result is a generalization of the representation for the…
This paper establishes characterization results for dynamic return and star-shaped risk measures induced via backward stochastic differential equations (BSDEs). We first characterize a general family of static star-shaped functionals in a…
In this paper, we study the well-posedness of backward doubly stochastic differential equations (BDSDEs), both with and without reflection, under weak conditions. First, when the generator $f$ is of general growth in $y$ and linear growth…
We prove the existence and uniqueness of viscosity solutions to quasi-variational inequalities (QVIs) with both upper and lower obstacles. In contrast to most previous works, we allow all involved coefficients to depend on the state…
In the present article we provide existence, uniqueness and stability results under an exponential moments condition for quadratic semimartingale backward stochastic differential equations (BSDEs) having convex generators. We show that the…
We introduce a domination argument which asserts that: if we can dominate theparameters of a quadratic backward stochastic differential equation (QBSDE) with continuousgenerator from above and from below by those of two BSDEs having ordered…
In this paper, we study continuous properties of adapted solutions for backward stochastic differential equations with constraints (CBSDEs in short). Comparing with many existing literatures about this topic, our case is very general in the…
In this paper, we first prove existence and uniqueness of the solution of a backward doubly stochastic differential equation (BDSDE) and of the related stochastic partial differential equation (SPDE) under monotonicity assumption on the…
In this paper, we first study one-dimensional quadratic backward stochastic differential equations driven by $G$-Brownian motions ($G$-BSDEs) with unbounded terminal values. With the help of a $\theta$-method of Briand and Hu [4] and…