EconPapers    
Economics at your fingertips  
 

A Dual Characterisation of Regulatory Arbitrage for Coherent Risk Measures

Martin Herdegen and Nazem Khan

Papers from arXiv.org

Abstract: We revisit mean-risk portfolio selection in a one-period financial market where risk is quantified by a positively homogeneous risk measure $\rho$ on $L^1$. We first show that under mild assumptions, the set of optimal portfolios for a fixed return is nonempty and compact. However, unlike in classical mean-variance portfolio selection, it can happen that no efficient portfolios exist. We call this situation regulatory arbitrage, and prove that it cannot be excluded - unless $\rho$ is as conservative as the worst-case risk measure. After providing a primal characterisation, we focus our attention on coherent risk measures, and give a necessary and sufficient characterisation for regulatory arbitrage. We show that the presence or absence of regulatory arbitrage for $\rho$ is intimately linked to the interplay between the set of equivalent martingale measures (EMMs) for the discounted risky assets and the set of absolutely continuous measures in the dual representation of $\rho$. A special case of our result shows that the market does not admit regulatory arbitrage for Expected Shortfall at level $\alpha$ if and only if there exists an EMM $\mathbb{Q} \approx \mathbb{P}$ such that $\Vert \frac{\text{d}\mathbb{Q}}{\text{d}\mathbb{P}} \Vert_{\infty}

Date: 2020-09
New Economics Papers: this item is included in nep-rmg
References: View references in EconPapers View complete reference list from CitEc
Citations: Track citations by RSS feed

Downloads: (external link)
http://arxiv.org/pdf/2009.05498 Latest version (application/pdf)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:arx:papers:2009.05498

Access Statistics for this paper

More papers in Papers from arXiv.org
Bibliographic data for series maintained by arXiv administrators ().

 
Page updated 2020-10-23
Handle: RePEc:arx:papers:2009.05498