【作者】 蔡立刚；

【导师】 李春吉；

【作者基本信息】 东北大学 ， 运筹学与控制论， 2008， 硕士

【摘要】 通过对随机过程中的矩方程上应用一个非常简明的变换,能够使用Euler-lagrange变分方法解决一些随机最优控制问题。严格的说,Euler-lagrange变分方法在随机最优控制问题中并不实用,它必须借助数值函数的方法,并且在实际问题中所得到的偏微分方程并不易解。而本文通过将矩问题引入变分方法中,使得新的状态变量是原状态变量的普通样本,变化后的动态方程和目标函数可以通过变分方法,得到对一个常微分方程的解,在某些实际问题中易解。本文将这个方法应用于经济中的随机需求下商品的零售商订货策略问题,投资组合及消费选择的最优控制问题,以及再保险模型的最优控制策略问题。在随机需求下商品的零售商订货策略问题中,结合市场需求的随机性,考虑价格的变动,以零售商期望利润最大化为出发点,寻求最优的订货策略。在投资组合及消费选择的最优控制问题中,为使得消费和终值财富的期望效用最大化,对给定时域的投资和消费给出最优解。在再保险模型的最优控制策略问题中,通过对一类带分红过程的比例再保险模型进行分析,采取最优控制策略。更多还原

【Abstract】 By using a very simple remark on the moment equations of stochastic processes, one can use the Euler-Lagrange variational approach to solve some stochastic optimal control problems. In stochastic optimal control, strictly speaking, Euler-Lagrange variational calculus does not apply, and one has to use value function approach. Unfortunately, on the practical standpoint, the partial differential equation so obtained is not very manageable. In the approach, the new state variable is the deviation from the nominal trajectory. The new dynamical equation and the new cost functions may be translated into the deterministic problem of a differential equation, and it is easy to solve. In the thesis, this approach is applicated in the stochastic economics, which include the problem on the retailer’s ordering policy for commodities with stochastic demand, the optimal investment and consumption problem and the optimal control policy of reinsurance model.In the first problem,the thesis studies inventory management of commodities according to the research of stochastic demand with service income management on perishable commodities in network environment, which aims to find order quantity that maximizes the retailer’s expected profit with stochastic demand.In the second problem, the optimal investment and consumption problem is to maximize the expected-utility about the consumption and terminal wealth extreme in fixed time domail.At last, we discuss a class of proportional reinsurance model with dividend process and also provide their optimal policies.更多还原