Abstract
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.
Citation
Hiroaki Hata. Hideo Nagai. Shuenn-Jyi Sheu. "Asymptotics of the probability minimizing a “down-side” risk." Ann. Appl. Probab. 20 (1) 52 - 89, February 2010. https://doi.org/10.1214/09-AAP618
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