73 citations · 235 across the 20 of their papers we have counts for
20 papers
On an Ergodic Two-Sided Singular Control Problem
Khwanchai Kunwai, Fubao Xi, George Yin +1
Motivated by applications in natural resource management, risk management, and finance, this paper is focused on an ergodic two-sided singular control problem for a general one-dim…
On Strong Feller Property, Exponential Ergodicity and Large Deviations Principle for Stochastic Damping Hamiltonian Systems with State-Dependent Switching
Fubao Xi, Chao Zhu, Fuke Wu
This work focuses on a class of stochastic damping Hamiltonian systems with state-dependent switching, where the switching process has a countably infinite state space. After estab…
Closed-loop Equilibrium for Time-Inconsistent McKean-Vlasov Controlled Problem
Hongwei Mei, Chao Zhu
The paper deals with a class of time-inconsistent control problems for McKean-Vlasov dynamics. By solving a backward time-inconsistent Hamilton-Jacobi-Bellman (HJB for short) equat…
On Feller and Strong Feller Properties and Irreducibility of Regime-Switching Jump Diffusion Processes with Countable Regimes
Khwanchai Kunwai, Chao Zhu
This work focuses on a class of regime-switching jump diffusion processes with a countably infinite state space for the discrete component. Such processes can be used to model comp…
Regime-Switching Jump Diffusions with Non-Lipschitz Coefficients and Countably Many Switching States: Existence and Uniqueness, Feller, and Strong Feller Properties
Fubao Xi, George Yin, Chao Zhu
This work focuses on a class of regime-switching jump diffusion processes, which is a two component Markov processes , where is a component representing discret…
On the Martingale Problem and Feller and Strong Feller Properties for Weakly Coupled Lévy Type Operators
Fubao Xi, Chao Zhu
This paper considers the martingale problem for a class of weakly coupled Lévy type operators. It is shown that under some mild conditions, the martingale problem is well-posed and…
Certain Properties Related to Well Posedness of Switching Diffusions
Dang H Nguyen, George Yin, Chao Zhu
This work is devoted to switching diffusions that have two components (a continuous component and a discrete component). Different from the so-called Markovian switching diffusions…
Almost Sure and Moment Exponential Stability of Regime-Switching Jump Diffusions
Zhen Chao, Kai Wang, Chao Zhu +1
This work is devoted to almost sure and moment exponential stability of regime-switching jump diffusions. The Lyapunov function method is used to derive sufficient conditions for s…
Jump Type Stochastic Differential Equations with Non-Lipschitz Coefficients: Non Confluence, Feller and Strong Feller Properties, and Exponential Ergodicity
Fubao Xi, Chao Zhu
This paper considers multidimensional jump type stochastic differential equations with super linear growth and non-Lipschitz coefficients. After establishing a sufficient condition…
Feynman-Kac Formulas for Regime-Switching Jump Diffusions and their Applications
Chao Zhu, George Yin, Nicholas A. Baran
This work develops Feynman-Kac formulas for a class of regime-switching jump diffusion processes, in which the jump part is driven by a Poisson random measure associated to a gener…
On Feller and Strong Feller Properties and Exponential Ergodicity of Regime-Switching Jump Diffusion Processes with Countable Regimes
Fubao Xi, Chao Zhu
This work focuses on a class of regime-switching jump diffusion processes, in which the switching component has countably infinite many states or regimes. The existence and uniquen…
A Counterintuitive Example in Inventory Management
Kurt L. Helmes, Richard H. Stockbridge, Chao Zhu
The paper \cite{helm:17} studies an inventory management problem under a long-term average cost criterion using weak convergence methods applied to average expected occupation and…
The Stochastic Solution to a Cauchy Problem for Degenerate Parabolic Equations
Xiaoshan Chen, Yu-Jui Huang, Qingshuo Song +1
We study the stochastic solution to a Cauchy problem for a degenerate parabolic equation arising from option pricing. When the diffusion coefficient of the underlying price process…
On Singular Control Problems with State Constraints and Regime-Switching: A Viscosity Solution Approach
Qingshuo Song, Chao Zhu
This paper investigates a singular stochastic control problem for a multi-dimensional regime-switching diffusion process confined in an unbounded domain. The objective is to maximi…
Numerical Solutions of Optimal Risk Control and Dividend Optimization Policies under A Generalized Singular Control Formulation
Zhuo Jin, George Yin, Chao Zhu
This paper develops numerical methods for finding optimal dividend pay-out and reinsurance policies. A generalized singular control formulation of surplus and discounted payoff fun…
On Optimal Harvesting in Stochastic Environments: Optimal Policies in a Relaxed Model
Richard H. Stockbridge, Chao Zhu
This paper examines the objective of optimally harvesting a single species in a stochastic environment. This problem has previously been analyzed in Alvarez (2000) using dynamic pr…
Optimal Dividend Payments for the Piecewise-Deterministic Poisson Risk Model
Runhuan Feng, Hans Volkmer, Shuaiqi Zhang +1
This paper considers the optimal dividend payment problem in piecewise-deterministic compound Poisson risk models. The objective is to maximize the expected discounted dividend pay…
Optimal control of risk process in a regime-switching environment
Chao Zhu
This paper is concerned with cost optimization of an insurance company. The surplus of the insurance company is modeled by a controlled regime switching diffusion, where the regime…
On Optimal Harvesting Problems in Random Environments
Qingshuo Song, Richard Stockbridge, Chao Zhu
This paper investigates the optimal harvesting strategy for a single species living in random environments whose growth is given by a regime-switching diffusion. Harvesting acts as…
Utility Maximization of an Indivisible Market with Transaction Costs
Qingshuo Song, G. Yin, Chao Zhu
This work takes up the challenges of utility maximization problem when the market is indivisible and the transaction costs are included. First there is a so-called solvency region…