2014/11/11 by Jingnan Fan, Fan, Jingnan, Andrzej Ruszczyński +1
Decision Sciences · Economics, Econometrics and Finance · Social Sciences · #49L20 #90C40 #FOS: Economics and business #FOS: Mathematics #Insurance, Mortality, Demography, Risk Management #Optimization and Control (math.OC) #Portfolio Management (q-fin.PM) #Risk and Portfolio Optimization #Stochastic processes and financial applications
paper · pdf · doi:10.48550/arxiv.1411.2675
openalex publication_date 2014/11/11 · openalex created_date 2016/12/16 · openalex updated_date 2026/07/28
For controlled discrete-time stochastic processes we introduce a new class of dynamic risk measures, which we call process-based. Their main features are that they measure risk of processes that are functions of the history of a base process. We introduce a new concept of conditional stochastic time consistency and we derive the structure of process-based risk measures enjoying this property. We show that they can be equivalently represented by a collection of static law-invariant risk measures on the space of functions of the state of the base process. We apply this result to controlled Markov processes and we derive dynamic programming equations.