Ergodic Risk-sensitive control -- A survey

TL;DR

This survey reviews four decades of research on ergodic risk-sensitive control, highlighting its significance in managing fluctuations, its links to $H_ fty$ control, and applications in financial mathematics.

Contribution

It provides a comprehensive overview of the development and key results in ergodic risk-sensitive control over the past forty years.

Findings

Extensive research has established the importance of ergodic risk-sensitive control.

Connections between risk-sensitive control and $H_ Infinity$ control are well-documented.

Applications in financial mathematics demonstrate practical relevance.

Abstract

Risk-sensitive control has received considerable interest since the seminal work of Howard and Matheson [120] because of its ability to account for fluctuations about the mean, its connection with $H_\infty$ control, and its application to financial mathematics. In this article, we attempt to put together a comprehensive survey on the research done on ergodic risk-sensitive control over the last four decades.