Existence and Uniqueness for Non-Markovian Triangular Quadratic BSDEs
نویسندگان
چکیده
We prove the existence and uniqueness of solutions to a class quadratic backward SDE (BSDE) systems which we call triangular quadratic. Our results generalize several existing about diagonally BSDEs in non-Markovian setting. As part our analysis, obtain new linear with unbounded coefficients, may be independent interest. Through nonuniqueness example, answer “crucial open question” raised by Harter Richou showing that stochastic exponential an $n \times n$ matrix-valued bounded mean oscillation martingale need not satisfy reverse Hölder inequality.
منابع مشابه
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...
متن کاملA 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...
متن کاملNon-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...
متن کاملOn 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].
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Siam Journal on Control and Optimization
سال: 2022
ISSN: ['0363-0129', '1095-7138']
DOI: https://doi.org/10.1137/21m1435689