最小化“下降”风险的概率的渐近性
Asymptotics of the probability minimizing a "down-side" risk
摘要：
我们考虑一个长期的最优投资问题，投资者试图最大限度地减少低于目标增长率的概率。从数学观点看，这是一个大偏差控制问题。这个问题将被证明涉及到一个风险敏感的随机控制问题，一个足够大的时间范围。事实上，在我们的定理中，我们陈述了上述两个问题之间关系的对偶性。此外，在多维线性高斯模型下，我们得到了原始问题的显式解。
英文摘要：
We consider a long-term optimal investment problem where an investor tries to minimize the probability of falling below a target growth rate. From a mathematical viewpoint, this is a large deviation control problem. This problem will be shown to relate to a risk-sensitive stochastic control problem for a sufficiently large time horizon. Indeed, in our theorem we state a duality in the relation between the above two problems. Furthermore, under a multidimensional linear Gaussian model we obtain explicit solutions for the primal problem.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
