Dynamic capital allocation rules via BSDEs: an axiomatic approach

TL;DR

This paper develops a new axiomatic framework for dynamic capital allocation rules using BSDEs, extending existing static and dynamic approaches and addressing gaps in the literature.

Contribution

It introduces a general axiomatic approach to dynamic capital allocations and explores methods for risk measures induced by g-expectations under weaker assumptions.

Findings

Proposes a novel axiomatic framework for dynamic capital allocation.

Extends the theory to risk measures induced by g-expectations.

Addresses limitations of gradient-based approaches in dynamic settings.

Abstract

In this paper, we study capital allocation for dynamic risk measures, with an axiomatic approach but also by exploiting the relation between risk measures and BSDEs. Although there is a wide literature on capital allocation rules in a static setting and on dynamic risk measures, only a few recent papers on capital allocation work in a dynamic setting and, moreover, those papers mainly focus on the gradient approach. To fill this gap, we then discuss new perspectives to the capital allocation problem going beyond those already existing in the literature. In particular, we introduce and investigate a general axiomatic approach to dynamic capital allocations as well as an approach suitable for risk measures induced by g-expectations under weaker assumptions than Gateaux differentiability.