English

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)

R2 v1 2026-06-21T14:34:09.049Z