Omega ratio optimization with actuarial and financial applications

Alejandro Balbás, Beatriz Balbás and Raquel Balbás

European Journal of Operational Research, 2021, vol. 292, issue 1, 376-387

Abstract: The omega ratio is an interesting performance measure because it focuses on both downside losses and upside gains, and actuarial/financial instruments are reflecting more and more asymmetry and heavy tails. This paper focuses on the omega ratio optimization in general Banach spaces, which applies for both infinite-dimensional approaches and more classical ones. New Fritz John-like and Karush Kuhn Tucker-like optimality conditions and duality results will be provided, despite the fact that omega is neither differentiable nor convex. Then, the focus is on both portfolio selection and optimal reinsurance, classic problems in Financial Mathematics and Actuarial Mathematics, respectively. The new duality results apply in order to study the potential ill-posedness of the financial problem. It will be provided further evidence about the relationship between the ill-posedness of problems involving omega and the ill-posedness of alternative problems avoiding omega and only involving coherent risk measures. The new optimality conditions apply in order to characterize and solve the actuarial problem. The solution is often a “bang-bang reinsurance contract”, i.e., a contract saturating the constraints of the ceded risk sensitivity with respect to the global (ceded plus retained) risk. In this sense, omega may be “essentially similar” to other deviation/downside risk measures previously studied, though the use of omega will also provoke some modifications in the final optimal results.

Keywords: Finance; Omega ratio; Optimality conditions; Unbounded financial problems; Optimal reinsurance (search for similar items in EconPapers)
Date: 2021
References: Add references at CitEc
Citations:

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0377221720308997
Full text for ScienceDirect subscribers only

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:eee:ejores:v:292:y:2021:i:1:p:376-387

DOI: 10.1016/j.ejor.2020.10.023

Access Statistics for this article

European Journal of Operational Research is currently edited by Roman Slowinski, Jesus Artalejo, Jean-Charles. Billaut, Robert Dyson and Lorenzo Peccati

More articles in European Journal of Operational Research from Elsevier
Bibliographic data for series maintained by Catherine Liu ().