Risk measures for processes and BSDEs

TL;DR

This paper develops a systematic framework for assessing risk in continuous-time cash flows using convex risk measures for processes, linking them to BSDEs and addressing model ambiguity and time value uncertainty.

Contribution

It introduces a dual representation for convex risk measures for processes and connects these measures to backward stochastic differential equations (BSDEs).

Findings

Provides a dual representation of convex risk measures for processes.

Establishes a link between risk measures for processes and BSDEs.

Addresses model ambiguity and time value uncertainty systematically.

Abstract

The paper analyzes risk assessment for cash flows in continuous time using the notion of convex risk measures for processes. By combining a decomposition result for optional measures, and a dual representation of a convex risk measure for bounded \cd processes, we show that this framework provides a systematic approach to the both issues of model ambiguity, and uncertainty about the time value of money. We also establish a link between risk measures for processes and BSDEs.