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Related papers: BSDEs with nonlinear weak terminal condition

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In this paper we study a class of backward stochastic differential equations (BSDEs) of the form dY(t)= -AY(t)dt -f_0(t,Y(t))dt -f_1(t,Y(t),Z(t))dt + Z(t)dW(t) on the interval [0,T], with given final condition at time T, in an infinite…

Probability · Mathematics 2007-05-23 Fulvia Confortola

In this paper, we study a class of reflected backward stochastic differential equations (BSDEs) of mean-field type, where the mean-field interaction in terms of the distribution of the $Y$-component of the solution enters in both the driver…

Probability · Mathematics 2019-11-15 Boualem Djehiche , Romuald Elie , Said Hamadène

The canonical theory of sublinear expectations, a foundation of stochastic calculus under ambiguity, is insensitive to the non-convex geometry of primitive uncertainty models. This paper develops a new stochastic calculus for a structured…

Probability · Mathematics 2025-07-31 Qian Qi

We consider a class of backward stochastic differential equations (BSDEs) with singular terminal condition and develop a numerical scheme to approximate their solution. To this end, we extend an asymptotic development of the BSDE solution…

Optimization and Control · Mathematics 2026-03-03 Thomas Kruse , Julia Ackermann , Alexandre Popier

We study a class of nonlinear BSDEs with a superlinear driver process f adapted to a filtration F and over a random time interval [[0, S]] where S is a stopping time of F. The terminal condition $\xi$ is allowed to take the value +$\infty$,…

Analysis of PDEs · Mathematics 2020-11-11 Alexandre Popier , Sharoy Samuel , Ali Sezer

This paper continues our previous work (Part I, arXiv:2504.18632v3) on the well-posedness of backward stochastic differential equations (BSDEs) involving a nonlinear Young integral of the form $\int_{t}^{T}g(Y_{r})\eta(dr,X_{r})$, with…

Probability · Mathematics 2025-09-08 Jian Song , Huilin Zhang , Kuan Zhang

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…

Probability · Mathematics 2013-12-16 Samuel Drapeau , Gregor Heyne , Michael Kupper

This paper is concerned with the stochastic Hamilton-Jacobi-Bellman equation with controlled leading coefficients, which is a type of fully nonlinear backward stochastic partial differential equation (BSPDE for short). In order to formulate…

Optimization and Control · Mathematics 2015-03-23 Jinniao Qiu

In the present paper, we consider multidimensional nonlinear backward stochastic differential equations (BSDEs) with a driver depending on the martingale part $M$ of a solution. We assume that the nonlinear term is merely monotone…

Probability · Mathematics 2023-08-22 Tomasz Klimsiak , Maurycy Rzymowski

In this paper, we study the backward stochastic differential equation (BSDE) with two nonlinear mean reflections, which means that the constraints are imposed on the distribution of the solution but not on its paths. Based on the backward…

Probability · Mathematics 2023-07-13 Hanwu Li

In this paper, we provide a one-to-one correspondence between the solution Y of a BSDE with singular terminal condition and the solution H of a BSDE with singular generator. This result provides the precise asymptotic behavior of Y close to…

Probability · Mathematics 2020-03-17 Paulwin Graewe , Alexandre Popier

We demonstrate that backward stochastic differential equations (BSDE) may be reformulated as ordinary functional differential equations on certain path spaces. In this framework, neither It\^{o}'s integrals nor martingale representation…

Probability · Mathematics 2012-11-20 Gechun Liang , Terry Lyons , Zhongmin Qian

In this paper we consider backward stochastic differential equations with time-delayed generators of a moving average type. The classical framework with linear generators depending on $(Y(t),Z(t))$ is extended and we investigate linear…

Pricing of Securities · Quantitative Finance 2011-07-13 Łukasz Delong

We provide existence results and comparison principles for solutions of backward stochastic difference equations (BS$\Delta$Es) and then prove convergence of these to solutions of backward stochastic differential equations (BSDEs) when the…

Probability · Mathematics 2013-07-24 Patrick Cheridito , Mitja Stadje

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…

Probability · Mathematics 2026-03-17 Shuxian Gao , Ying Hu , Jiaqiang Wen

We study a new class of ergodic backward stochastic differential equations (EBSDEs for short) which is linked with semi-linear Neumann type boundary value problems related to ergodic phenomenas. The particularity of these problems is that…

Probability · Mathematics 2010-02-11 Adrien Richou

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…

Probability · Mathematics 2010-07-12 Samuel N. Cohen , Robert J. Elliott

We are interested in stochastic control problems coming from mathematical finance and, in particular, related to model uncertainty, where the uncertainty affects both volatility and intensity. This kind of stochastic control problems is…

Probability · Mathematics 2014-05-15 Sébastien Choukroun , Andrea Cosso

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…

Probability · Mathematics 2015-12-29 T Kruse , A Popier

In this paper, we consider the Cauchy problem of semi-linear degenerate backward stochastic partial differential equations (BSPDEs in short) under general settings without technical assumptions on the coefficients. For the solution of…

Probability · Mathematics 2011-09-06 Kai Du , Qi Zhang