03:30 PM - 03:55 PM
Dynamic optimal strategies in transboundary pollution game with abatement policy and emission permits trading
Environmental issues are becoming more and more important. This paper obtains optimal emission levels and abatement expenditures in a finite-horizon transboundary pollution game with emission trading between two regions.. We work out the players' revenues over time, and show that emission trading has a great influence on the optimal strategies and revenues of the two regions. We also find that cooperation between the regions leads to increased abatement and lower emissions, resulting in a lower pollution stock. We also provide a stochastic extension in which the pollution stock and emission trading price are diffusion processes, and solve it numerically.
03:55 PM - 04:20 PM
Dynamic optimal decision making for manufacturers with limited attention based on sparse dynamic programming
In a fully competitive industry, manufacturers is required to respond rapidly to market demand, and hence it is utter important for them to manage their inventory effectively as well as to determine the best order quantity and optimal productivity. In this paper, we consider the situation where the manufacturers with limited attention is to determine the optimal order quantity and the optimal productivity when many factors are volatile, such as the price of raw materials or finished goods, attrition rate of inventory of raw materials or finished product (according to various empirical studies, it is observed that decision makers tend to focus their attention on factors with large changes). This problem is formulated as a discrete-time stochastic dynamic programming problem. We propose a general method based on the sparse dynamic programming method to solve this discrete-time multidimensional stochastic dynamic programming problem. From the numerical examples being solved using the proposed method, it is interesting to observe that decision makers with limited attention do not adjust the final decision when the volatility is small.
04:20 PM - 04:45 PM
Asymptotic stability for a fractured rock reservoir model
We consider a problem arising in oil recovery simulation in fractured rock reservoir. This problem models the fluid flow, where the history of the flow is considered. Most of the existing papers on related works mainly treats the convergence of solutions to the equilibrium state without establishing any decay rate. Using the modified energy method, we improve and extend the existing results by weakening the conditions leading to exponential decay. The type of decays and the underlying spaces are extended to more general decays and more regular spaces.