2022/03/17 by Ziteng Cheng, Cheng, Ziteng, Sebastian Jaimungal +1
Decision Sciences · Economics, Econometrics and Finance · Social Sciences · #FOS: Economics and business #FOS: Mathematics #Insurance and Financial Risk Management #Insurance, Mortality, Demography, Risk Management #Mathematical Finance (q-fin.MF) #Optimization and Control (math.OC) #Risk Management (q-fin.RM) #Risk and Portfolio Optimization
paper · pdf · doi:10.48550/arxiv.2203.09612
openalex publication_date 2022/03/17 · openalex created_date 2022/05/27 · openalex updated_date 2026/07/28
By adopting a distributional viewpoint on law-invariant convex risk measures, we construct dynamics risk measures (DRMs) at the distributional level. We then apply these DRMs to investigate Markov decision processes, incorporating latent costs, random actions, and weakly continuous transition kernels. Furthermore, the proposed DRMs allow risk aversion to change dynamically. Under mild assumptions, we derive a dynamic programming principle and show the existence of an optimal policy in both finite and infinite time horizons. Moreover, we provide a sufficient condition for the optimality of deterministic actions. For illustration, we conclude the paper with examples from optimal liquidation with limit order books and autonomous driving.