【作者】 王庆；

【导师】 戴万阳；

【作者基本信息】 南京大学 ， 基础数学， 2012， 硕士

【摘要】 本文主要考虑由二维随机微分方程驱动的最优机制转换问题.其方法是通过泰勒展开将由该随机微分方程的无穷小生成元得到的二元偏微分方程转化为含参量的一元常微分方程组,并利用该方程组得到了一个新的随机微分方程.再借助于现存解决有关一元最优机制转换问题的方法并且利用所涉及的边界条件,我们得到了有关二元最优机制转换问题的近似解,它包含了近似最优价值函数与近似最优转换时刻的确定及随机动态规划的求解等.更多还原

【Abstract】 In this paper we consider the optimal switching mechanism driven by2-dimensional stochastic differential equation. We try to convert a2-variable partial differential equation, which is acquired by the infinitesimal generator of the above stochastic differential equation, into a1-variable ordinary differential equations, by means of Taylor expansion. Then we obtain a new stochastic differential equation, and, with the boundary conditions involved, we get an approximative solution of the2-variable optimal switching mechanism, following existing methods for solving the1-variable optimal switching mechanism. The solution consists of the de-termination of approximative optimal value function and approximative optimal switching time, and the solvement of the stochastic dynamical programming, etc.更多还原