A note on representation of BSDE-based dynamic risk measures and dynamic capital allocations

Abstract

We derive a representation for dynamic capital allocation when the underlying asset price process includes extreme random price movements. Moreover, we consider the representation of dynamic risk measures defined under Backward Stochastic Differential Equations (BSDE) with generators that grow quadratic-exponentially in the control variables. Dynamic capital allocation is derived from the differentiability of BSDEs with jumps. The results are illustrated by deriving a capital allocation representation for dynamic entropic risk measure and static coherent risk measure.

Keywords:

• Dynamic risk capital allocation
• dynamic risk measure
• quadratic-exponential BSDE
• dynamic entropic risk measure

Acknowledgements

We would like to thank the following sponsors University of Pretoria, UCDP-MSS Program, Simons Africa, NRF, DST-Risk and the MCTESTP Mozambique for their support.

Notes

1 Note that H is the Cameron-Martin space defined in Appendix.

Additional information

Funding

This work was supported by National Research Foundation.