%0 Journal Article
%T Characterization of the minimal penalty of a convex risk measure with applications to Levy processes
%A Daniel Hern¨˘ndez-Hern¨˘ndez
%A Leonel P¨¦rez-Hern¨˘ndez
%J Mathematics
%D 2012
%I arXiv
%X The minimality of the penalization function associated with a convex risk measure is analyzed in this paper. First, in a general static framework, we provide necessary and sufficient conditions for a penalty function defined in a convex and closed subset of the absolutely continuous measures with respect to some reference measure $\mathbb{P}$ to be minimal. When the probability space supports a L\'{e}vy process, we establish results that guarantee the minimality property of a penalty function described in terms of the coefficients associated with the density processes. The set of densities processes is described and the convergence of its quadratic variation is analyzed.
%U http://arxiv.org/abs/1205.3827v2