Asymptotics of the probability minimizing a "down-side" risk
Probability
2010-01-14 v1 Computational Finance
Portfolio Management
Risk Management
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.
Keywords
Cite
@article{arxiv.1001.2131,
title = {Asymptotics of the probability minimizing a "down-side" risk},
author = {Hiroaki Hata and Hideo Nagai and Shuenn-Jyi Sheu},
journal= {arXiv preprint arXiv:1001.2131},
year = {2010}
}
Comments
Published in at http://dx.doi.org/10.1214/09-AAP618 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org)