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J. Backhoff, L. Tangpi:
"On the dynamic representation of some time-inconsistent risk measures in a Brownian filtration";
arXiv.org, September (2017), 28 pages.

It is well-known from the work of Kupper and Schachermayer that m
ost risk measures do not admit a time-consistent representation. In this work we show that in a Brownian filtration
the "Optimized Certainty Equivalent" risk measures of Ben-Tal and
Teboulle can be computed through PDE techniques, that is, dynamically. This can be seen as a s
ubstitute of sorts whenever they lack time consistency, and covers the cases of conditional value-at-risk and monotone mean-
variance. Our results apply directly in the Markovian setting but we p
rovide evidence showing that our approach can be applied to general claims. Our method consists of first extending the state
space, and then using stochastic control techniques along with th
e theory of viscosity solutions.

Time-inconsistency risk measures optimized certainty equivalent HJB equation viscosity supersolution unbounded stochastic control problem

https://arxiv.org/abs/1608.07498?context=math.OC