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Related papers: A new comparison theorem of multidimensional BSDEs

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In this paper we first prove a general representation theorem for generators of backward stochastic differential equations (BSDEs for short) by utilizing a localization method involved with stopping time tools and approximation techniques,…

Probability · Mathematics 2017-01-17 Lishun Xiao , Shengjun Fan

The present paper is devoted to the well-posedness of a type of multi-dimensional backward stochastic differential equations (BSDEs) with a diagonally quadratic generator. We give a new priori estimate, and prove that the BSDE admits a…

Probability · Mathematics 2024-04-17 Guang Yang

We study non-linear Backward Stochastic Differential Equations (BSDEs) driven by a Brownian motion and p default martingales. The driver of the BSDE with multiple default jumps can take a generalized form involving an optional finite…

Mathematical Finance · Quantitative Finance 2026-01-06 Miryana Grigorova , James Wheeldon

In this paper, we study the multi-dimensional mean-field backward stochastic differential equations (BSDEs, for short) with quadratic growth. Under small terminal value, the existence and uniqueness are proved for the multi-dimensional…

Probability · Mathematics 2022-08-15 Tao Hao , Jiaqiang Wen , Jie Xiong

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…

Probability · Mathematics 2008-07-08 Stefan Ankirchner , Peter Imkeller , Alexandre Popier

We consider a backward stochastic differential equation with a generator that can be subjected to delay, in the sense that its current value depends on the weighted past values of the solutions, for instance a distorted recent average.…

Probability · Mathematics 2015-09-08 Peng Luo , Ludovic Tangpi

In this paper, the notion of singular backward stochastic Volterra integral equations (singular BSVIEs for short) in infinite dimensional space is introduced, and the corresponding well-posedness is carefully established. A class of…

Optimization and Control · Mathematics 2023-12-08 Tianxiao Wang , Mengliang Zheng

We study an optimal execution problem in illiquid markets with both instantaneous and persistent price impact and stochastic resilience when only absolutely continuous trading strategies are admissible. In our model the value function can…

Optimization and Control · Mathematics 2017-11-30 Paulwin Graewe , Ulrich Horst

We introduce a new type of reflected backward stochastic differential equations (BSDEs) for which the reflection constraint is imposed on its main solution component, denoted as $Y$ by convention, but in terms of its conditional expectation…

Probability · Mathematics 2022-11-15 Ying Hu , Jianhui Huang , Wenqiang Li

We study the properties of nonlinear Backward Stochastic Differential Equations (BSDEs) driven by a Brownian motion and a martingale measure associated with a default jump with intensity process $(\lambda_t)$. We give a priori estimates for…

Pricing of Securities · Quantitative Finance 2017-09-04 Roxana Dumitrescu , Marie-Claire Quenez , Agnès Sulem

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…

Probability · Mathematics 2012-06-04 Na Zhang , Guangyan Jia

A new asymptotic expansion scheme for backward SDEs (BSDEs) is proposed.The perturbation parameter is introduced just to scale the forward stochastic variables within a BSDE. In contrast to the standard small-diffusion asymptotic expansion…

Computational Finance · Quantitative Finance 2014-12-23 Masaaki Fujii

This paper establishes an existence and uniqueness result for the adapted solution of a general time interval multidimensional backward stochastic differential equation (BSDE), where the generator $g$ satisfies a weak…

Probability · Mathematics 2019-11-27 Tingting Li , Ziheng Xu , Shengjun Fan

We investigate a class of quadratic backward stochastic differential equations (BSDEs) with generators singular in $ y $. First, we establish the existence of solutions and a comparison theorem, thereby extending results in the literature.…

Probability · Mathematics 2025-03-17 Wenbo Wang , Guangyan Jia

We propose the Compound BSDE method, a fully forward, deep-learning-based approach for solving a broad class of problems in financial mathematics, including optimal stopping. The method is based on a reformulation of option pricing problems…

Computational Finance · Quantitative Finance 2026-02-02 Zhipeng Huang , Cornelis W. Oosterlee

In this paper, we generalize to Gaussian Volterra processes the existence and uniqueness of solutions for a class of non linear backward stochastic differential equations (BSDE) and we establish the relation between the non linear BSDE and…

Probability · Mathematics 2020-05-15 Habiba Knani

In this note, we study one-dimensional reflected backward doubly stochastic differential equations (RBDSDEs) with one continuous barrier and discontinuous generator (left-or right-continuous). By a comparison theorem establish here for…

Probability · Mathematics 2010-11-16 Auguste Aman , Jean Marc Owo

We study Backward Stochastic Differential Equations on a probability space equipped with a Brownian filtration. We assume that the terminal value and the generator at zero are merely integrable. Moreover, the generator is assumed to be…

Probability · Mathematics 2022-08-09 Tomasz Klimsiak , Maurycy Rzymowski

We study a multi-dimensional optimal execution problem in illiquid markets with both instantaneous and persistent price impact and stochastic resilience. In our model the value function can be described by a multi-dimensional backward…

Optimization and Control · Mathematics 2018-09-07 Ulrich Horst , Xiaonyu Xia

This paper investigates McKean-Vlasov backward stochastic variational inequalities (BSVIs) whose generator depends on the joint law of the solution. We first establish the existence and uniqueness of the solution under globally Lipschitz…

Optimization and Control · Mathematics 2026-04-03 Qi Liu , Yanbo Chen