2013/12/04 by Tomasz R. Bielecki, Bielecki, Tomasz R., Igor Cialenco +3
Decision Sciences · Economics, Econometrics and Finance · Mathematics · #62P05 #91B06 #91B30 #97M30 #Economic theories and models #FOS: Economics and business #FOS: Mathematics #Probability (math.PR) #Risk Management (q-fin.RM) #Risk and Portfolio Optimization #Stochastic processes and financial applications #math.PR #msc:62P05 #msc:91B06 #msc:91B30 #msc:97M30 #q-fin.RM
paper · pdf · doi:10.48550/arxiv.1312.1006
openalex publication_date 2013/12/04 · arxiv created 2014/07/21 · arxiv updated 2014/07/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We propose a new class of mappings, called Dynamic Limit Growth Indices, that are designed to measure the long-run performance of a financial portfolio in discrete time setup. We study various important properties for this new class of measures, and in particular, we provide necessary and sufficient condition for a Dynamic Limit Growth Index to be a dynamic assessment index. We also establish their connection with classical dynamic acceptability indices, and we show how to construct examples of Dynamic Limit Growth Indices using dynamic risk measures and dynamic certainty equivalents. Finally, we propose a new definition of time consistency, suitable for these indices, and we study time consistency for the most notable representative of this class -- the dynamic analog of risk sensitive criterion.