Abstract
In this paper, we propose the notion of dynamic deviation measure, as a dynamic time-consistent extension of the (static) notion of deviation measure. To achieve time-consistency, we require that a dynamic deviation measures satisfies a generalised conditional variance formula. We show that, under a domination condition, dynamic deviation measures are characterised as the solutions to a certain class of stochastic differential equations. We establish for any dynamic deviation measure an integral representation, and derive a dual characterisation result in terms of additively
Citation
Martijn Pistorius. Mitja Stadje. "On dynamic deviation measures and continuous-time portfolio optimization." Ann. Appl. Probab. 27 (6) 3342 - 3384, December 2017. https://doi.org/10.1214/17-AAP1282
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