A stochastic control problem with delay arising in a pension fund model
A stochastic control problem with delay arising in a pension fund model
复制标题
DOI：
10.1007/s00780-010-0146-4
复制
发表时间：
2011-09
影响因子：
1.7
通讯作者：
S. Federico
中科院分区：
文献类型：
--
作者：
S. Federico
本文研究了一类随机时滞微分方程的最优控制问题。这个问题是接近的工具表示在无限维。我们证明了一维时滞问题和相应的无限维无时滞问题之间的等价性。然后我们证明了值函数在无限维的情况下是连续的。这些结果代表了一个起点，调查相关的无穷维Hamilton-Jacobi-Bellman方程的粘性意义上，并接近问题的数值算法。最后给出了一个较简单但类似问题的完整解的例子。
This paper deals with the optimal control of a stochastic delay differential equation arising in the management of a pension fund with surplus. The problem is approached by the tool of a representation in infinite dimension. We show the equivalence between the one-dimensional delay problem and the associated infinite-dimensional problem without delay. Then we prove that the value function is continuous in this infinite-dimensional setting. These results represent a starting point for the investigation of the associated infinite-dimensional Hamilton–Jacobi–Bellman equation in the viscosity sense and for approaching the problem by numerical algorithms. Also an example with complete solution of a simpler but similar problem is provided.