We study a coherent version of the entropic risk measure, both in the law-invariant case and in a situation of model ambiguity. In particular, we discuss its behavior under the pooling of independent risks and its connection with a classical and a robust large deviations bound.
This paper provides an introduction to the theory of capital requirements defined by convex risk measures. The emphasis is on robust representations, law-invariant convex risk measures and their robustification in the face of model uncertainty, asymptotics for large portfolios, and on the connections of convex risk measures to actuarial premium principles and robust preferences.
For a stochastic factor model we maximize the long-term growth rate of robust
expected power utility with parameter $\lambda\in(0,1)$. Using duality methods
the problem is reformulated as an infinite time horizon, risk-sensitive control
problem. Our results characterize the optimal growth rate, an optimal long-term
trading strategy and an asymptotic worst-case model in terms of an ergodic
Bellman equation. With these results we propose a duality approach to a "robust
large deviations" criterion for optimal long-term investment.Comment: Published in at http://dx.doi.org/10.1214/11-AAP764 the Annals of
Applied Probability (http://www.imstat.org/aap/) by the Institute of
Mathematical Statistics (http://www.imstat.org
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