Acceptability Indices of Performance for Bounded C\`adl\`ag Processes

TL;DR

This paper extends acceptability indices to bounded cadlag processes modeling cash flows, proposing a new RAROC-type index based on static and dynamic risk measures, with numerical comparisons illustrating its performance evaluation capabilities.

Contribution

It introduces a novel acceptability index for cadlag processes combining static and dynamic risk measures, and provides a representation theorem for bounded paths.

Findings

Proposes a RAROC-type acceptability index for processes.

Provides a representation result for bounded cadlag paths.

Includes numerical comparisons demonstrating the index's effectiveness.

Abstract

Indices of acceptability are well suited to frame the axiomatic features of many performance measures, associated to terminal random cash flows.We extend this notion to classes of c\`adl\`ag processes modelling cash flows over a fixed investment horizon.We provide a representation result for bounded paths. We suggest an acceptability index based both on the static Average Value-at-Risk functional and the running minimum of the paths, which eventually represents a RAROC-type model. Some numerical comparisons clarify the magnitude of performance evaluation for processes.