On the two-times differentiability of the value functions in the problem of optimal investment in incomplete markets
成果类型：
Article
署名作者：
Kramkov, Dmitry; Sirbu, Mihai
署名单位：
Carnegie Mellon University; Columbia University
刊物名称：
ANNALS OF APPLIED PROBABILITY
ISSN/ISSBN：
1050-5164
DOI：
10.1214/105051606000000259
发表日期：
2006
页码：
1352-1384
关键词：
摘要：
We study the two-times differentiability of the value functions of the primal and dual optimization problems that appear in the setting of expected utility maximization in incomplete markets. We also study the differentiability of the solutions to these problems with respect to their initial values. We show that the key conditions for the results to hold true are that the relative risk aversion coefficient of the utility function is uniformly bounded away from zero and infinity, and that the prices of traded securities are sigma-bounded under the numeraire given by the optimal wealth process.