POLLUTION, GOVERNMENT EXPENDITURE, TAXES AND STOCHASTIC GROWTH

This paper studies a stochastic endogenous growth model with pollution. It introduces government expenditure and exogenous pollution abatement technology to eliminate pollution and proves that under appropriate equilibrium conditions the main economic indexes （including economic growth rate, the optimal government expenditure rate） in the centrally planned economy and decentralized economy can be expressed by the parameters of the model uniquely. The optimal tax policy is analyzed ,and the optimal pollution is derived.

Distributive Disturbance and Optimal Policy in Stochastic Control Model

To investigate the equilibrium relationships between the volatility of capital and income, taxation, and ance in a stochastic control model, the uniqueness of the solution to this model was proved by using the method of dynamic programming under the introduction of distributive disturbance and elastic labor supply. Furthermore, the effects of two types of shocks on labor-leisure choice, economic growth rate and welfare were numerically analyzed, and then the optimal tax policy was derived.

Stochastic Control Model on Rent Seeking

A continuous-time stochastic model is constructed to analyze how to control rent seeking behaviors. Using the stochastic optimization methods based on the modem risky theory, a unique positive solution to the dynamic model is derived. The effects of preference-related parameters on the optimal control level of rent seeking are discussed, and some policy measures are given. The results show that there exists a unique solution to the stochastic dynamic model under some macroeconomic assumptions, and that raising public expenditure may have reverse effects on rent seeking in an underdeveloped or developed economic environment.

AN OPTION PRICING MODEL UNDER FUTURE REVENUE UNCERTAINTY

The purpose of this paper is to discuss how the value of high-tech firm can be rationally valued by taking into account managerial flexibility when its future revenue is uncertain,thereby the firm's manager can make rational investment decisions.Using stochastic control theory,the paper will present that the firm's value satisfies a partially differentiate equation,and analyze the managerial flexibility value within a framework of real-option analytic theorey.Finally,the comparative static analysis and the model's simple application are given.

Pricing Bermudan Option with Variable Transaction Costs under the Information-Based Model

The Bermudan option pricing problem with variable transaction costs is considered for a risky asset whose price process is derived under the information-based model. The price is formulated as the value function of an optimal stopping problem, which is the value function of a stochastic control problem given by a non-linear second order partial differential equation. The theory of viscosity solutions is applied to solve the stochastic control problem such that the value function is also the solution of the corresponding Bellman equation. Under some regularity assumptions, the existence and uniqueness of the solution of the pricing equation are derived by the application of the Perron method and Banach Fixed Point theorem.

基于Q Learning算法的区域配网业务路由分配方法研究

传统的配网业务路由分配方法的链条占用率过高,导致丢包率较大。为此,设计了基于Q Learning算法的区域配网业务路由分配方法。按照传统分类方式划分业务路由中的性能指标,根据路由约束条件计算指标的约束值,从而确定业务路由的最优传输路径。结合Bellman Equation方法不断计算并更新配网中的Q值,再综合节点和网络业务指标,利用Q Learning算法计算得到区域配网中的风险均衡度。不断变换VNFs的路由顺序将其转换为TSP路由问题,最终得到路由分配矩阵,实现区域配网业务路由的分配。实验结果表明:与传统分配方法相比,基于Q Learning算法的分配方法的链条占用率低,有效减小了业务数据转发过程的丢包率。

Moving least-squares approximations for linearly-solvable stochastic optimal control problems

Nonlinear stochastic optimal control problems are fundamental in control theory.A general class of such problems can be reduced to computing the principal eigenfunction of a linear operator.Here,we describe a new method for finding this eigenfunction using a moving least-squares function approximation.We use efficient iterative solvers that do not require matrix factorization,thereby allowing us to handle large numbers of basis functions.The bases are evaluated at collocation states that change over iterations of the algorithm,so as to provide higher resolution at the regions of state space that are visited more often.The shape of the bases is automatically defined given the collocation states,in a way that avoids gaps in the coverage.Numerical results on test problems are provided.

Optimal Reinsurance and Investment Strategy with Delay in Heston’s SV Model

In this paper,we consider an optimal investment and proportional reinsurance problem with delay,in which the insurer’s surplus process is described by a jump-diffusion model.The insurer can buy proportional reinsurance to transfer part of the insurance claims risk.In addition to reinsurance,she also can invests her surplus in a financial market,which is consisted of a risk-free asset and a risky asset described by Heston’s stochastic volatility(SV)model.Considering the performance-related capital flow,the insurer’s wealth process is modeled by a stochastic differential delay equation.The insurer’s target is to find the optimal investment and proportional reinsurance strategy to maximize the expected exponential utility of combined terminal wealth.We explicitly derive the optimal strategy and the value function.Finally,we provide some numerical examples to illustrate our results.