On the equivalence between Value-at-Risk and Expected Shortfall in non-concave optimization
An Chen,
Mitja Stadje and
Fangyuan Zhang
Papers from arXiv.org
Abstract:
This paper studies an optimal asset allocation problem for a surplus-driven financial institution facing a Value-at-Risk (VaR) or an Expected Shortfall (ES) constraint corresponding to a non-concave optimization problem under constraints. We obtain the closed-form optimal wealth with the ES constraint as well as with the VaR constraint respectively, and explicitly calculate the optimal trading strategy for constant relative risk aversion (CRRA) utility functions. We find that both VaR and ES-based regulation can effectively reduce the probability of default for a surplus-driven financial institution. However, the liability holders' benefits cannot be fully protected under either VaR- or ES-based regulation. In addition, we show that the VaR and ES-based regulation can induce the same optimal portfolio choice for a surplus-driven financial institution. This differs from the conclusion drawn in Basak and Shapiro 2001 where the financial institution aims at maximizing the expected utility of the total assets, and ES provides better loss protection.
Date: 2020-02, Revised 2020-08
New Economics Papers: this item is included in nep-rmg and nep-upt
References: View references in EconPapers View complete reference list from CitEc
Citations: Track citations by RSS feed
Downloads: (external link)
http://arxiv.org/pdf/2002.02229 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:2002.02229
Access Statistics for this paper
More papers in Papers from arXiv.org
Bibliographic data for series maintained by arXiv administrators ().