Optimal Strategies for Risk-Sensitive Portfolio Optimization Problems for General Factor Models
Optimal Strategies for Risk-Sensitive Portfolio Optimization Problems for General Factor Models
复制标题
DOI：
10.1137/s0363012901399337
复制
发表时间：
2002-06
期刊：
影响因子：
--
通讯作者：
H. Nagai
中科院分区：
文献类型：
--
作者：
H. Nagai
我们考虑构建一般因子模型的无限时间范围内的风险敏感投资组合优化问题的最优策略，其中单个证券或资产类别的平均收益率和波动率明显受到经济因素的影响。这些因素被假定为一般的扩散过程。在研究风险敏感投资组合优化问题的各态历经型Bellman方程时，我们引入了一些辅助的经典随机控制问题，这些随机控制问题具有与原问题相同的Bellman方程。我们证明了问题的最优扩散过程是遍历的，并且在与扩散过程的不变测度的可积性有关的某些条件下，我们可以通过使用Bellman方程的解来构造原问题的最优策略。
We consider constructing optimal strategies for risk-sensitive portfolio optimization problems on an infinite time horizon for general factor models, where the mean returns and the volatilities of individual securities or asset categories are explicitly affected by economic factors. The factors are assumed to be general diffusion processes. In studying the ergodic type Bellman equations of the risk-sensitive portfolio optimization problems, we introduce some auxiliary classical stochastic control problems with the same Bellman equations as the original ones. We show that the optimal diffusion processes of the problem are ergodic and that under some condition related to integrability by the invariant measures of the diffusion processes we can construct optimal strategies for the original problems by using the solution of the Bellman equations.