最优策略

By investigating the convexity, monotonicity and asymptotic behaviour of the optimal value function, it is shown that the optimal policy is of simple hedging point structure and featured by several hedging points.

通过研究最优值函数的凸性、单调性和渐近性，证明了最优策略具有简单的阈值结构且被几个阈值参数完全刻画。

Moreover, in order to find the optimal control strategy we propose optimal control models and obtain optimality conditions.

此外为了寻找最优策略，建立了最优控制模型，研究了最优控制问题的最优性条件。

We can use value iteration to obtain the optimal value function, from which the optimal policy can be derived efficiently.

用值迭代的方法可以求解MDP的最优值函数，然后从最优值函数得到最优策略。

By exploring the properties of the optimal value function, several simple and realistic sub-optimal policies are presented.These sub-optimal policies are of threshold structure, which are featured only by a number of threshold parameters.

分析了生产两种品种的纸机的最优策略的结构品质，提出了一种简易可行的次优控制策略：阈值控制策略。

Operations research ; batchselling ; optimal strategy ; optimal revenue value function

运筹学；分批销售；最优策略；最优收益值函数

Unified field, mixed extension principle, optimal strategy solution of the games, utility function and utility functional, pure strategy, mixed strategy

统一场，混合扩充原理，博弈的最优策略解，效用函数与效用泛函，纯策略，混合策略

The problem has been studied from two sides, firstly, from the viewpoint of applicability, based on the development strategic objectives of the oil company, with the aim to unify the exploration and extraction decisions of the resources in an integrated framework, and integrate the macro economic and technical objectives with micro economic and technical models of an oil well, an integrated non-linear dynamic optimal control model has been constructed, the objective is the benefit maximum of the exploration and extraction of the resources, and the optimalstrategies are obtained by changing the problem into a non-linear mathematical programming problem, on the other hand, from the more macro level, based on the analysis of the characteristics of the exploration and extraction activities of oil and gas resources, a conclusion is easily deduced that the procedure is full of randomicity, then discovering procedure of oil deposit is proved to be a Poisson process, and the reserves process is a supermartingale process, so the model of exploration discovery rate and the reserves model could be constructed.

其次从相对更宏观的层次上，通过对油气资源勘探与开发的特点分析，认为具有很强的随机性，证明了勘探活动发现油气藏的过程为一泊松过程，所发现的油气藏储量为一上鞅过程，在此基础上，建立了油气藏勘探发现率模型及储量模型，在油气价格服从几何布朗运动条件下，以油气开采收益最大化为目标，建立了一个油气资源勘探与开发的随机最优控制模型，采用动态规划方法得到了值函数的HJB方程，并针对方程的特点，以及方程及其变量所对应的经济学意义，对最优策略的求解进行了一些讨论。

We show that the solutions for the HARA utility are stable in the sense of weak convergence when the parameters vary in a suitable way.

当效用函数为HARA、指数和对数型时，我们分别得到了最优投资的显式解，并且证明了当HARA效用函数中的参数变化时所对应的最优策略在弱收敛意义下的稳定性。

Simulation results are included to show that the optimal policy given by this method can well approach to the accurate one given by value iterative method on the case of having complete information, and the constringent rate of policy is quickly than others.

仿真表明，该算法所求解的控制策略与用值迭代法在模型已知的情况下，所求得的最优策略非常逼近，且该算法使得策略的收敛速度大大地加快了。

The optimal dynamic unlimited excess of loss reinsurance using the mean-variance premium principle is studied. Following Hipp's theory, a corresponding Hamilton-Jacobi-Bellman equation is obtained to minimize the ruin probability, and existence and optimality of the solution is proved.

考虑具有均值－方差保费原理的超额损失再保险的最优策略问题，沿用Hipp的理论框架，以最小化破产概率为目标，得到一个Hamilton-Jacobi-Bellman方程，并证明了其解的存在性及最优性。

Breath, muscle contraction of the buttocks; arch body, as far as possible to hold his head, right leg straight towards the ceiling (peg-leg knee in order to avoid muscle tension).

呼气，收缩臀部肌肉；拱起身体，尽量抬起头来，右腿伸直朝向天花板（膝微屈，以避免肌肉紧张）。

The cost of moving grain food products was unchanged from May, but year over year are up 8%.

粮食产品的运输费用与5月份相比没有变化，但却比去年同期高8％。