Optimal stopping problems with discontinous reward: Regularity of the value function and viscosity solutions
Optimal stopping problems with discontinous reward: Regularity of the value function and viscosity solutions
复制标题
具有不连续奖励的最优停止问题：价值函数的正则性和粘度解
DOI：
10.1080/10451120290008557
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发表时间：
2002
期刊：
影响因子：
--
通讯作者：
Claudia Ceci
中科院分区：
文献类型：
--
作者：
Bruno Bassan;Claudia Ceci
研究了报酬函数不连续的扩散过程的最优停止问题。我们给出了一些关于价值函数的正则性的结果，并证明了在适当的温和条件下，它具有与奖励函数相同的正则性，即，如果奖励函数为，则它是下（分别为：上）连续的。这两种情况的证明是完全不同的，并且上连续的情况需要更强的条件。最后，我们证明了，在较低的连续报酬的情况下，在适当的条件下，值函数是一个（不连续）粘性解的相关变分不等式。
We study optimal stopping problems for diffusion processes with discontinuous reward function. We give some results about the regularity of the value function and we show that, under suitable mild conditions on the underlying process, it has the same regularity of the reward function, namely, it is lower (respectively: upper) semicontinuous if the reward function is. The proofs for the two cases are quite different, and the upper semicontinuous case requires stronger conditions. Finally, we show that, in the case of lower semicontinuous reward, under suitable conditions the value function is a (discontinuous) viscosity solution of the associated variational inequalities.