2015/12/11 by Elisa Mastrogiacomo, Mastrogiacomo, Elisa, Emanuela Rosazza Gianin +1
Decision Sciences · Economics, Econometrics and Finance · Social Sciences · #46A20 #60G44 #91B30 #91G30 #FOS: Economics and business #FOS: Mathematics #Insurance, Mortality, Demography, Risk Management #Mathematical Finance (q-fin.MF) #Probability (math.PR) #Risk Management (q-fin.RM) #Risk and Portfolio Optimization #Stochastic processes and financial applications
paper · pdf · doi:10.48550/arxiv.1512.03641
openalex publication_date 2015/12/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The main goal of this paper is to investigate under which conditions cash-subadditive convex dynamic risk measures are time-consistent. Proceeding as in Detlefsen and Scandolo \citedetlef-scandolo and inspired by their result, we give a dual representation of dynamic cash-subadditive convex risk measures (that can also be seen as particular case of the dual quasiconvex representation). The main result of the paper consists in providing, in the cash-subadditive case, a sufficient condition for strong time-consistency (or recursivity) in terms of a generalized cocycle condition. On one hand, our result can be seen as an extension to cash-subadditive convex dynamic risk measures of Theorem 2.5 in Bion-Nadal \citebion-nadal-FS; on the other hand, it is weaker since strong time-consistency is not fully characterized. Finally, we exploit the relation between different notions of time-consistency.