360 research outputs found
Downside risk minimization via a large deviations approach
We consider minimizing the probability of falling below a target growth rate
of the wealth process up to a time horizon in an incomplete market model,
and then study the asymptotic behavior of minimizing probability as
. This problem can be closely related to an ergodic risk-sensitive
stochastic control problem in the risk-averse case. Indeed, in our main
theorem, we relate the former problem concerning the asymptotics for risk
minimization to the latter as its dual. As a result, we obtain an expression of
the limit value of the probability as the Legendre transform of the value of
the control problem, which is characterized as the solution to an H-J-B
equation of ergodic type, in the case of a Markovian incomplete market model.Comment: Published in at http://dx.doi.org/10.1214/11-AAP781 the Annals of
Applied Probability (http://www.imstat.org/aap/) by the Institute of
Mathematical Statistics (http://www.imstat.org
On an exponential character of the spectral distribution function of a random difference operator
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