Asymptotics of the probability minimizing a "down-side" risk

Details Asymptotics of the probability minimizing a "down-side" risk Asymptotics of the probability minimizing a "down-side" risk

2010-01-13

arxiv.org/abs/1001.2131v1

Annals of Applied Probability 2010, Vol. 20, No. 1, 52-89

Mathematics

Probability

Published in at http://dx.doi.org/10.1214/09-AAP618 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Inst

Scientific paper

10.1214/09-AAP618

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.

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