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.
Publié le : 2010-02-15
Classification:
Large deviation,
long-term investment,
risk-sensitive stochastic control,
Bellman equation,
35J60,
49L20,
60F10,
91B28,
93E20
@article{1262962318,
author = {Hata, Hiroaki and Nagai, Hideo and Sheu, Shuenn-Jyi},
title = {Asymptotics of the probability minimizing a ``down-side'' risk},
journal = {Ann. Appl. Probab.},
volume = {20},
number = {1},
year = {2010},
pages = { 52-89},
language = {en},
url = {http://dml.mathdoc.fr/item/1262962318}
}
Hata, Hiroaki; Nagai, Hideo; Sheu, Shuenn-Jyi. Asymptotics of the probability minimizing a “down-side” risk. Ann. Appl. Probab., Tome 20 (2010) no. 1, pp. 52-89. http://gdmltest.u-ga.fr/item/1262962318/