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

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.

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)

References in corpus (1)

• On the structure of solutions of ergodic type Bellman equation related to risk-sensitive control

Cited by in corpus (2)

• Downside risk minimization via a large deviations approach
• Asymptotics of robust utility maximization