Existence and Uniqueness for Non-Markovian Triangular Quadratic BSDEs

Markovian quadratic and superquadratic BSDEs with an unbounded terminal condition

A Note on Existence and Uniqueness for Solutions of Multidimensional Reflected Bsdes

The theory of Backward Stochastic Differential Equations (BSDEs for short) offers a large number of applications in the field of stochastic control or mathematical finance. Recently, Hu and Tang [4] introduced and studied a new type of BSDE, constrained by oblique reflections, and associated to optimal switching problems. Via heavy arguments, Hamadène and Zhang [3] generalized the form of these...

A uniqueness theorem for solution of BSDEs

where W is a standard d-dimensional Brownian motion on a probability space (Ω,F , (Ft)0≤t≤T , P ) with (Ft)0≤t≤T the filtration generated by W . The function g : Ω × [0, T ] × R × R → R is called generator of (1.1). Here T is the terminal time, and ξ is a R-valued FT -adapted random variable; (g, T, ξ) are the parameters of (1.1). The solution (yt, zt)t∈[0,T ] is a pair of Ft-adapted and square...

Non-existence and Non-uniqueness for Multidimensional Sticky Particle Systems

The paper is concerned with sticky weak solutions to the equations of pressureless gases in two or more space dimensions. Various initial data are constructed, showing that the Cauchy problem can have (i) two distinct sticky solutions, or (ii) no sticky solution, not even locally in time. In both cases the initial density is smooth with compact support, while the initial velocity field is conti...

On the uniqueness of solutions to quadratic BSDEs with convex generators and unbounded terminal conditions

In [4], the authors proved the uniqueness among the solutions which admit every exponential moments. In this paper, we prove that uniqueness holds among solutions which admit some given exponential moments. These exponential moments are natural as they are given by the existence theorem. Thanks to this uniqueness result we can strengthen the nonlinear Feynman-Kac formula proved in [4].