Markov risk mappings and risk-sensitive optimal prediction
Optimization and Control
2022-09-05 v4 Probability
Mathematical Finance
Abstract
We formulate a probabilistic Markov property in discrete time under a dynamic risk framework with minimal assumptions. This is useful for recursive solutions to risk-sensitive versions of dynamic optimisation problems such as optimal prediction, where at each stage the recursion depends on the whole future. The property holds for standard measures of risk used in practice, and is formulated in several equivalent versions including a representation via acceptance sets, a strong version, and a dual representation.
Cite
@article{arxiv.2001.06895,
title = {Markov risk mappings and risk-sensitive optimal prediction},
author = {Tomasz Kosmala and Randall Martyr and John Moriarty},
journal= {arXiv preprint arXiv:2001.06895},
year = {2022}
}
Comments
21 pages. Improved introduction and a new result on the canonical form for a Markovian family of dynamic risk measures