Abstract : This minisymposium features new developments in stochastic analysis, control, and their applications. The invited speakers will be presenting results on impulse control with discontinuous setup costs, deep learning approach for optimal control, optimal control problem for regime-switching processes, and feedback control for switching diffusion systems based on discrete time observations in the first session. The second session will be focused on exponential stability and weak stability of stochastic functional differential equations with impulsive perturbations and a two-time-scale formulation as well as McKean-Vlasov stochastic differential equations. It is anticipated that this minisymposium will help to exchange ideas and stimulate further collaborations.
[03197] Continuous-Review Inventory Systems with Discontinuous Setup Costs
Format : Talk at Waseda University
Author(s) :
Dacheng Yao (Academy of Mathematics and Systems Science, Chinese Academy of Sciences)
Abstract : In this talk, we will discuss continuous-review inventory systems, in which the setup cost of each order is a discontinuous function of order quantity and the demand process is modeled as a Brownian motion with a positive drift. Assuming the holding and shortage cost to be a convex function of inventory level, we prove that an (s, S) policy is optimal among all admissible policies under the long-run average cost criterion. However, under the discounted cost criterion, we find that although some (s, S)-type policies are indeed optimal in some cases, any (s, S) policy cannot always be optimal for all initial inventory level x∊R in the other cases.
[04097] Deep learning methods in insurance and risk management
Format : Online Talk on Zoom
Author(s) :
Zhuo Jin (Macquarie University)
Abstract : Recently, deep learning approaches has drawn increasing attention in decision making processes. A type of Markov chain approximation-based iterative deep learning algorithm is developed to study the optimal control problems arising from the insurance industry. The optimal controls are approximated as deep neural networks. The framework of Markov chain approximation plays a key role in building the iterative equations and initialization of the algorithm. Optimal parameters of neural networks are then obtained iteratively.
[04139] Exponential stability of stochastic functional differential equations with impulsive perturbations
Format : Talk at Waseda University
Author(s) :
KY QUAN TRAN (SUNY Korea)
George Yin (University of Connecticut)
Abstract : This work aims to investigate the moment exponential stability of stochastic functional differential equations subject to
impulsive perturbations and Markovian switching. In contrast to existing literature, we propose new criteria for moment exponential stability and a new method for computing moment Lyapunov exponents. Our analysis also shows that the Euler-Maruyama approximation method can effectively reproduce exponential stability in the mean square, provided
that the step sizes are sufficiently small.
[03618] Fully-coupled two-time-scale stochastic functional differential equations with infinite delay
Format : Talk at Waseda University
Author(s) :
Fuke Wu (Huazhong University of Science and Technology)
Abstract : This paper examines the fully-coupled two-time-scale stochastic functional differential equations (SFDEs) with infinite delay. The system under consideration involves a slow component and a fast component. This paper aims to establish the averaging principle. To overcome the difficulty due to the infinite delay and the coupling of the segment process, some properties as the Hölder continuity and tightness on a space of continuous functions have to be investigated for the segment process.
[03662] On the weak stability and stabilization of McKean-Vlasov stochastic differential equations
Format : Talk at Waseda University
Author(s) :
Chao Zhu (University of Wisconsin-Milwaukee)
Abstract : This work focuses on weak stability and stabilization of a class of McKean-Vlasov stochastic differential equations (SDEs). First, under suitable conditions on the coefficients of the SDE, we derive explicit quantitative contraction rates for the convergence in Wasserstein distances of McKean-Vlasov SDEs using the coupling method. The contraction results are then used to prove a propagation of chaos uniformly in time, which provides quantitative bounds on convergence rate of interacting particle systems, and establishes exponential ergodicity for McKean-Vlasov SDEs. Finally we consider the question of stabilizing in the weak sense an arbitrary McKean-Vlasov SDE using suitable feedback controls with delays.
[05067] Limit Theorems for Distribution Dependent Jump Processes with Random Switching
Format : Online Talk on Zoom
Author(s) :
Fubao Xi (Beijing Institute of Technology)
Chao Zhu (University of Wisconsin-Milwaukee)
Abstract : We consider distribution dependent jump processes with random switching, where the switching processes may have a countably infinite state space. By virtue of the martingale approach, we first establish the existence and uniqueness theorem of the underlying processes for a special Markovian switching case. Using a martingale function, we then transfer the existence and uniqueness result onto the general state-dependent switching case. Moreover, we establish two limit theorems for the processes with mean field interactions.
[03342] From the optimal singular stochastic control to the optimal stopping for regime-switching processes
Format : Online Talk on Zoom
Author(s) :
Jinghai Shao (Tianjin University)
Taoran Tian (Tianjin University)
Abstract : This work generalizes the connection between optimal singular control and optimal stopping problem for regime-switching processes. Via optimal singular control, the optimal stopping time and the continuation region are characterized. Moreover, we prove the existence of optimal singular stochastic control for a finite horizon singular control problem with the cost function containing the terminal cost. We prove it directly by the compactification method. Such a problem was left open in Haussmann and Suo (SICON, 1995).
