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Related papers: Quadratic Mean-Field BSDEs and Exponential Utility…

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This paper studies a class of mean-field control (MFC) problems with singular controls under general dynamic state-control-law constraints. We first propose a customized relaxed control formulation to cope with the dynamic mixed constraints…

Optimization and Control · Mathematics 2026-04-28 Lijun Bo , Jingfei Wang , Xiang Yu

This article studies the sensitivity of the power utility maximization problem with respect to the investor's relative risk aversion, the statistical probability measure, the investment constraints and the market price of risk. We extend…

Optimization and Control · Mathematics 2011-07-04 Markus Mocha , Nicholas Westray

In the present paper we discuss a new type of mean-field coupled forward-backward stochastic differential equations (MFFBSDEs). The novelty consists in the fact that the coefficients of both the forward as well as the backward SDEs depend…

Probability · Mathematics 2023-07-27 Rainer Buckdahn , Juan Li , Junsong Li , Chuanzhi Xing

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…

Probability · Mathematics 2012-08-07 Markus Mocha , Nicholas Westray

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

Over the last few decades, the numerical methods for stochastic differential delay equations (SDDEs) have been investigated and developed by many scholars. Nevertheless, there is still little work to be completed. By virtue of the novel…

Numerical Analysis · Mathematics 2022-09-21 Zhuoqi Liu , Qian Guo , Shuaibin Gao

We analyze a class of multidimensional linear-quadratic stochastic control problems with random coefficients, motivated by multi-asset optimal trade execution. The problems feature non-diffusive controlled state dynamics and a terminal…

Optimization and Control · Mathematics 2026-01-08 Julia Ackermann , Thomas Kruse , Petr Petrov , Alexandre Popier

We consider a non-Markovian optimal stopping problem on finite horizon. We prove that the value process can be represented by means of a backward stochastic differential equation (BSDE), defined on an enlarged probability space, containing…

Probability · Mathematics 2015-02-20 Marco Fuhrman , Huyên Pham , Federica Zeni

In Liang et al (2009), the current authors demonstrated that BSDEs can be reformulated as functional differential equations, and as an application, they solved BSDEs on general filtered probability spaces. In this paper the authors continue…

Probability · Mathematics 2010-11-22 G. Liang , T. Lyons , Z. Qian

The paper establishes the exponential turnpike property for a class of mean-field stochastic linear-quadratic (LQ) optimal control problems with periodic coefficients. It first introduces the concepts of stability, stabilizability, and…

Optimization and Control · Mathematics 2024-07-26 Jingrui Sun , Lvning Yuan , Jiaqi Zhang

Connections between a system of Forward-Backward SDEs and Backward Stochastic PDEs related to the utility maximiza- tion problem is established. Besides, we derive another version of FBSDE of the same problem and prove an existence of a…

Probability · Mathematics 2018-02-06 Michael Mania , Revaz Tevzadze

In this article, we follow the study of quadratic backward SDEs with jumps,that is to say for which the generator has quadratic growth in the variables (z; u), started in our accompanying paper [15]. Relying on the existence and uniqueness…

Probability · Mathematics 2014-03-13 M. Nabil Kazi-Tani , Dylan Possamaï , Chao Zhou

The BMO martingale theory is extensively used to study nonlinear multi-dimensional stochastic equations (SEs) in $\cR^p$ ($p\in [1, \infty)$) and backward stochastic differential equations (BSDEs) in $\cR^p\times \cH^p$ ($p\in (1, \infty)$)…

Probability · Mathematics 2008-01-24 Freddy Delbaen , Shanjian Tang

We first establish the existence of an unbounded solution to a backward stochastic differential equation (BSDE) with generator $g$ allowing a general growth in the state variable $y$ and a sub-quadratic growth in the state variable $z$,…

Probability · Mathematics 2019-10-21 Shengjun Fan , Ying Hu

This paper is concerned with a backward-forward stochastic differential equation (BFSDE) system, in which a large number of negligible agents are coupled in their dynamics via state average. Here some BSDE is introduced as the dynamics of…

Optimization and Control · Mathematics 2014-03-18 Jianhui Huang , Shujun Wang , Zhen Wu

We address the Merton problem of maximizing the expected utility of terminal wealth using techniques from variational analysis. Under a general continuous semimartingale market model with stochastic parameters, we obtain a characterization…

Portfolio Management · Quantitative Finance 2020-03-20 Ali Al-Aradi , Sebastian Jaimungal

In this paper, we study one-dimensional backward stochastic differential equation (BSDE, for short), whose coefficient $f$ is Lipschitz in $y$ but only continuous in $z$. In addition, if the terminal condition $\xi$ has bounded Malliavin…

Probability · Mathematics 2022-08-09 Yufeng Shi , Zhi Yang

The present paper is devoted to the study of backward stochastic differential equations with mean reflection formulated by Briand et al. [7]. We investigate the solvability of a generalized mean reflected BSDE, whose driver also depends on…

Probability · Mathematics 2022-11-03 Ying Hu , Remi Moreau , Falei Wang

With the terminal value $\xi^-$ admitting a certain exponential moment and $\xi^+$ admitting every exponential moments or being bounded, we establish several existence and uniqueness results for unbounded solutions of backward stochastic…

Probability · Mathematics 2024-04-08 Yan Wang , Xinying Li , Chuang Gu , Shengjun Fan

We study the problem of existence of solutions for generalized backward stochastic differential equation with two reflecting barriers (GRBSDE for short) under weaker assumptions on the data. Roughly speaking we show the existence of a…

Probability · Mathematics 2011-03-29 E. H. Essaky , M. Hassani , Y. Ouknine