# Computational aspects of minimizing conditional value-at-risk

*Alexandra Künzi-Bay* () and
*János Mayer*

*Computational Management Science*, 2006, vol. 3, issue 1, 3-27

**Abstract:**
We consider optimization problems for minimizing conditional value-at-risk (CVaR) from a computational point of view, with an emphasis on financial applications. As a general solution approach, we suggest to reformulate these CVaR optimization problems as two-stage recourse problems of stochastic programming. Specializing the L-shaped method leads to a new algorithm for minimizing conditional value-at-risk. We implemented the algorithm as the solver CVaRMin. For illustrating the performance of this algorithm, we present some comparative computational results with two kinds of test problems. Firstly, we consider portfolio optimization problems with 5 random variables. Such problems involving conditional value at risk play an important role in financial risk management. Therefore, besides testing the performance of the proposed algorithm, we also present computational results of interest in finance. Secondly, with the explicit aim of testing algorithm performance, we also present comparative computational results with randomly generated test problems involving 50 random variables. In all our tests, the experimental solver, based on the new approach, outperformed by at least one order of magnitude all general-purpose solvers, with an accuracy of solution being in the same range as that with the LP solvers. Copyright Springer-Verlag Berlin/Heidelberg 2006

**Keywords:** Conditional value-at-risk; Stochastic programming; Mathematical programming algorithms; Stochastic models; Finance; Portfolio optimization; Risk management (search for similar items in EconPapers)

**Date:** 2006

**References:** Add references at CitEc

**Citations:** View citations in EconPapers (19) Track citations by RSS feed

**Downloads:** (external link)

http://hdl.handle.net/10.1007/s10287-005-0042-0 (text/html)

Access to full text is restricted to subscribers.

**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:spr:comgts:v:3:y:2006:i:1:p:3-27

**Ordering information:** This journal article can be ordered from

http://www.springer. ... ch/journal/10287/PS2

Access Statistics for this article

Computational Management Science is currently edited by *Ruediger Schultz*

More articles in Computational Management Science from Springer

Bibliographic data for series maintained by Sonal Shukla ().