Process-Based Risk Measures and Risk-Averse Control of Discrete-Time Systems
Optimization and Control
2016-11-30 v5 Portfolio Management
Abstract
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.
Cite
@article{arxiv.1411.2675,
title = {Process-Based Risk Measures and Risk-Averse Control of Discrete-Time Systems},
author = {Jingnan Fan and Andrzej Ruszczynski},
journal= {arXiv preprint arXiv:1411.2675},
year = {2016}
}