arXiv subjects

Zihao Gu

Publications and source records attributed to Zihao Gu.

5 recordsLinked to original sources

arXiv2026

On Information Controls

In this paper we study an optimization problem in which the control is information, more precisely, the control is a $\sigma$-algebra or a filtration. In a dynamic setting, we establish the dynamic programming principle and the law invariance of the value function. The latter requires a condition slightly stronger than the (H)-hypothesis for the admissible filtration, and enables us to define the value function on $\mathcal P_2(\mathcal P_2(\mathbb R^d))$, the space of laws of random probability measures. By using a new It\^o's formula for smooth functions on $\mathcal P_2(\mathcal P_2(\mathbb R^d))$, we characterize the value function of the information control problem by an Hamilton-Jacobi-Bellman equation on this space.

math.OC↗

arXiv2024

$G$-BSDEs with mean constraints in time-dependent intervals

In this paper, we study a collection of mean-reflected backward stochastic differential equations driven by $G$-Brownian motions ($G$-BSDEs), where $G$-expectations are constrained in some time-dependent intervals. To establish well-posedness results, we firstly construct a backward Skorokhod problem with sublinear expectation, and then apply that in the study of doubly mean-reflected $G$-BSDEs involving Lipschitz and quadratic generators under bounded and unbounded terminal conditions. Also we utilize fixed-point argumentations and $\theta$-methods while solving these equations. Finally, we extend the results to multi-dimensional doubly mean-reflected $G$-BSDEs with diagonal generators.

math.PR↗

arXiv2023

Reflected BSDE driven by a marked point process with a convex/concave generator

In this paper, a class of reflected backward stochastic differential equations (RBSDE) driven by a marked point process (MPP) with a convex/concave generator is studied. Based on fixed point argument, $\theta$-method and truncation technique, the well-posedness of this kind of RBSDE with unbounded terminal condition and obstacle is investigated. Besides, we present an application on the pricing of American options via utility maximization, which is solved by constructing an RBSDE with a convex generator.

math.PR↗

arXiv2023

Exponential growth BSDE driven by a marked point process

In this study, we investigate the well-posedness of exponential growth backward stochastic differential equations (BSDEs) driven by a marked point process (MPP) under unbounded terminal conditions. Our analysis utilizes a fixed-point argument, the $\theta$-method, and an approximation procedure. Additionally, we establish the solvability of mean-reflected exponential growth BSDEs driven by the MPP using the $\theta$-method.

math.PR↗

arXiv2023

Mean reflected BSDE driven by a marked point process and application in insurance risk management

This paper aims to solve a super-hedging problem along with insurance re-payment under running risk management constraints. The initial endowment for the super-heding problem is characterized by a class of mean reflected backward stochastic differential equation driven by a marked point process (MPP) and a Brownian motion. By Lipschitz assumptions on the generators and proper integrability on the terminal value, we give the well-posedness of this kind of BSDEs by combining a representation theorem with the fixed point argument.

math.PR↗