The Annals of Applied Probability
- Ann. Appl. Probab.
- Volume 22, Number 2 (2012), 608-669.
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 T in an incomplete market model, and then study the asymptotic behavior of minimizing probability as T → ∞. 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.
Ann. Appl. Probab., Volume 22, Number 2 (2012), 608-669.
First available in Project Euclid: 2 April 2012
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Nagai, Hideo. Downside risk minimization via a large deviations approach. Ann. Appl. Probab. 22 (2012), no. 2, 608--669. doi:10.1214/11-AAP781. https://projecteuclid.org/euclid.aoap/1333372009