相关论文: Bounded solutions to backward SDE's with jumps for…
We develop a multilevel approach to compute approximate solutions to backward differential equations (BSDEs). The fully implementable algorithm of our multilevel scheme constructs sequential martingale control variates along a sequence of…
This paper is concerned with a general non-homogeneous stochastic linear quadratic (LQ) control problem with regime switching and random coefficients. We obtain the explicit optimal state feedback control and optimal value for this problem…
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…
In this paper, we establish the invariance of observability for the observed backward stochastic differential equations (BSDEs) with constant coefficients, relative to the filtered probability space. This signifies that the observability of…
In this paper, we, for the first time, establish two comparison theorems for multi-dimensional backward stochastic differential equations with jumps. Our approach is novel and completely different from the existing results for…
In this paper, using the mean-field game theory, we study a problem of equilibrium price formation among many investors with exponential utility in the presence of liabilities unspanned by the security prices. The investors are…
We consider an optimal stochastic impulse control problem over an infinite time horizon motivated by a model of irreversible investment choices with fixed adjustment costs. By employing techniques of viscosity solutions and relying on…
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.…
This paper develops a probabilistic numerical method for solution of partial differential equations (PDEs) and studies application of that method to PDE-constrained inverse problems. This approach enables the solution of challenging inverse…
We propose new machine learning schemes for solving high dimensional nonlinear partial differential equations (PDEs). Relying on the classical backward stochastic differential equation (BSDE) representation of PDEs, our algorithms estimate…
Motivated from time-inconsistent stochastic control problems, we introduce a new type of coupled forward-backward stochastic systems, namely, flows of forward-backward stochastic differential equations. They are systems consisting of a…
The paper provides global optimization algorithms for two particularly difficult nonconvex problems raised by hybrid system identification: switching linear regression and bounded-error estimation. While most works focus on local…
The long time behaviour of solutions to generalised stochastic porous media equations on bounded domains with Dirichlet boundary data is studied. We focus on a degenerate form of nonlinearity arising in self-organised criticality. Based on…
A risk-neutral method is always used to price and hedge contingent claims in complete market, but another method based on utility maximization or risk minimization is wildly used in more general case. One can find all kinds of special risk…
In this paper we derive a novel characterization result for time-consistent stochastic control problems with higher-order moments, originally formulated by Wang et al. [SIAM J. Control. Optim., 63 (2025), 1560--1589], and newly explore many…
In this paper, we study an optimal mean-variance investment-reinsurance problem for an insurer (she) under a Cram\'er-Lundberg model with random coefficients. At any time, the insurer can purchase reinsurance or acquire new business and…
The study of optimal control problems under uncertainty plays an important role in scientific numerical simulations. This class of optimization problems is strongly utilized in engineering, biology and finance. In this paper, a stochastic…
This paper introduces a statistical treatment of inverse problems constrained by models with stochastic terms. The solution of the forward problem is given by a distribution represented numerically by an ensemble of simulations. The goal is…
This paper aims at solving one-dimensional backward stochastic differential equations (BSDEs) under weaker assumptions. We establish general existence, uniqueness, and comparison results for bounded solutions, $L^p (p>1)$ solutions and…
This paper is concerned with a Stackelberg game of backward stochastic differential equations (BSDEs), where the coefficients of the backward system and the cost functionals are deterministic, and the control domain is convex. Necessary and…