IDEAS home Printed from https://ideas.repec.org/p/cte/imrepe/id-16-01.html
   My bibliography  Save this paper

VaR as the CVaR sensitivity : applications in risk optimization

Author

Listed:
  • Balbás, Beatriz
  • Balbás, Raquel

Abstract

VaR minimization is a complex problem playing a critical role in many actuarial and financial applications of mathematical programming. The usual methods of convex programming do not apply due to the lack of sub-additivity. The usual methods of differentiable programming do not apply either, due to the lack of continuity. Taking into account that the CVaR may be given as an integral of VaR, one has that VaR becomes a first order mathematical derivative of CVaR. This property will enable us to give accurate approximations in VaR optimization, since the optimization VaR and CVaR will become quite closely related topics. Applications in both finance and insurance will be given.

Suggested Citation

  • Balbás, Beatriz & Balbás, Raquel, 2016. "VaR as the CVaR sensitivity : applications in risk optimization," IC3JM - Estudios = Working Papers id-16-01, Instituto Mixto Carlos III - Juan March de Ciencias Sociales (IC3JM).
    • Handle: RePEc:cte:imrepe:id-16-01
    as

    Download full text from publisher

    File URL: https://e-archivo.uc3m.es/rest/api/core/bitstreams/37b62e07-7a40-45c7-a12a-52777b033ebb/content
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. R. Rockafellar & Stan Uryasev & Michael Zabarankin, 2006. "Generalized deviations in risk analysis," Finance and Stochastics, Springer, vol. 10(1), pages 51-74, January.
    2. Hirbod Assa & Keivan Mallahi Karai, 2013. "Hedging, Pareto Optimality, and Good Deals," Journal of Optimization Theory and Applications, Springer, vol. 157(3), pages 900-917, June.
    3. Dean P. Foster & Sergiu Hart, 2009. "An Operational Measure of Riskiness," Journal of Political Economy, University of Chicago Press, vol. 117(5), pages 785-814.
    4. Robert J. Aumann & Roberto Serrano, 2008. "An Economic Index of Riskiness," Journal of Political Economy, University of Chicago Press, vol. 116(5), pages 810-836, October.
    5. Basak, Suleyman & Shapiro, Alexander, 2001. "Value-at-Risk-Based Risk Management: Optimal Policies and Asset Prices," The Review of Financial Studies, Society for Financial Studies, vol. 14(2), pages 371-405.
    6. William T. Shaw, 2011. "Risk, VaR, CVaR and their associated Portfolio Optimizations when Asset Returns have a Multivariate Student T Distribution," Papers 1102.5665, arXiv.org.
    7. Mitra, Sovan & Karathanasopoulos, Andreas & Sermpinis, Georgios & Dunis, Christian & Hood, John, 2015. "Operational risk: Emerging markets, sectors and measurement," European Journal of Operational Research, Elsevier, vol. 241(1), pages 122-132.
    8. Turan G. Bali & Nusret Cakici & Fousseni Chabi-Yo, 2011. "A Generalized Measure of Riskiness," Management Science, INFORMS, vol. 57(8), pages 1406-1423, August.
    9. Cai, Jun & Tan, Ken Seng, 2007. "Optimal Retention for a Stop-loss Reinsurance Under the VaR and CTE Risk Measures," ASTIN Bulletin, Cambridge University Press, vol. 37(1), pages 93-112, May.
    10. Philippe Artzner & Freddy Delbaen & Jean‐Marc Eber & David Heath, 1999. "Coherent Measures of Risk," Mathematical Finance, Wiley Blackwell, vol. 9(3), pages 203-228, July.
    11. Dupačová, Jitka & Kopa, Miloš, 2014. "Robustness of optimal portfolios under risk and stochastic dominance constraints," European Journal of Operational Research, Elsevier, vol. 234(2), pages 434-441.
    12. Annaert, Jan & Osselaer, Sofieke Van & Verstraete, Bert, 2009. "Performance evaluation of portfolio insurance strategies using stochastic dominance criteria," Journal of Banking & Finance, Elsevier, vol. 33(2), pages 272-280, February.
    13. Kaluszka, Marek, 2005. "Optimal reinsurance under convex principles of premium calculation," Insurance: Mathematics and Economics, Elsevier, vol. 36(3), pages 375-398, June.
    14. Andrzej Ruszczyński & Alexander Shapiro, 2006. "Optimization of Convex Risk Functions," Mathematics of Operations Research, INFORMS, vol. 31(3), pages 433-452, August.
    15. Chavez-Demoulin, V. & Embrechts, P. & Neslehova, J., 2006. "Quantitative models for operational risk: Extremes, dependence and aggregation," Journal of Banking & Finance, Elsevier, vol. 30(10), pages 2635-2658, October.
    16. Hirbod Assa, 2015. "Trade-off Between Robust Risk Measurement and Market Principles," Journal of Optimization Theory and Applications, Springer, vol. 166(1), pages 306-320, July.
    17. Chi, Yichun & Tan, Ken Seng, 2013. "Optimal reinsurance with general premium principles," Insurance: Mathematics and Economics, Elsevier, vol. 52(2), pages 180-189.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. repec:cte:idrepe:id-16-01 is not listed on IDEAS
    2. Balbás, Beatriz & Balbás, Raquel, 2013. "On the inefficiency of Brownian motions and heavier tailed price processes," IC3JM - Estudios = Working Papers id-13-01, Instituto Mixto Carlos III - Juan March de Ciencias Sociales (IC3JM).
    3. repec:cte:idrepe:id-13-01 is not listed on IDEAS
    4. repec:cte:idrepe:22932 is not listed on IDEAS
    5. Balbás, Beatriz & Balbás, Raquel, 2016. "Coherent Pricing," IC3JM - Estudios = Working Papers 22932, Instituto Mixto Carlos III - Juan March de Ciencias Sociales (IC3JM).
    6. Balbás, Alejandro & Balbás, Beatriz & Heras, Antonio, 2011. "Stable solutions for optimal reinsurance problems involving risk measures," European Journal of Operational Research, Elsevier, vol. 214(3), pages 796-804, November.
    7. Alejandro Balbas & Beatriz Balbas & Raquel Balbas, 2013. "Optimal Reinsurance: A Risk Sharing Approach," Risks, MDPI, vol. 1(2), pages 1-12, August.
    8. Balbás, Alejandro & Balbás, Beatriz & Heras, Antonio, 2009. "Optimal reinsurance with general risk measures," Insurance: Mathematics and Economics, Elsevier, vol. 44(3), pages 374-384, June.
    9. Balbás, Alejandro & Balbás, Beatriz & Balbás, Raquel & Heras, Antonio, 2015. "Optimal reinsurance under risk and uncertainty," Insurance: Mathematics and Economics, Elsevier, vol. 60(C), pages 61-74.
    10. Balbás, Beatriz & Heras, Antonio, 2010. "Stability of the optimal reinsurance with respect to the risk measure," DEE - Working Papers. Business Economics. WB wb100201, Universidad Carlos III de Madrid. Departamento de Economía de la Empresa.
    11. Balbás, Beatriz & Balbás, Raquel & Rodríguez de las Heras Pérez, Antonio, 2014. "Optimal reinsurance under risk and uncertainty," IC3JM - Estudios = Working Papers id-14-04, Instituto Mixto Carlos III - Juan March de Ciencias Sociales (IC3JM).
    12. repec:cte:idrepe:id-14-04 is not listed on IDEAS
    13. Balbás, Beatriz & Balbás, Raquel, 2016. "Must an optimal buy and hold strategy contain any derivative?," IC3JM - Estudios = Working Papers 23912, Instituto Mixto Carlos III - Juan March de Ciencias Sociales (IC3JM).
    14. Doron Nisani, 2023. "On the General Deviation Measure and the Gini coefficient," International Journal of Economic Theory, The International Society for Economic Theory, vol. 19(3), pages 599-610, September.
    15. Enrico G. De Giorgi & David B. Brown & Melvyn Sim, 2010. "Dual representation of choice and aspirational preferences," University of St. Gallen Department of Economics working paper series 2010 2010-07, Department of Economics, University of St. Gallen.
    16. Guerra, Manuel & Centeno, M.L., 2012. "Are quantile risk measures suitable for risk-transfer decisions?," Insurance: Mathematics and Economics, Elsevier, vol. 50(3), pages 446-461.
    17. Samuel Drapeau & Michael Kupper, 2013. "Risk Preferences and Their Robust Representation," Mathematics of Operations Research, INFORMS, vol. 38(1), pages 28-62, February.
    18. , & ,, 2015. "The Foster-Hart measure of riskiness for general gambles," Theoretical Economics, Econometric Society, vol. 10(1), January.
    19. Gustavo Silva Araújo & José Valentim Machado Vicente, 2014. "Indicadores Antecedentes Extraídos de Preços de Ativos em Corte Transversal," Working Papers Series 361, Central Bank of Brazil, Research Department.
    20. Balbás, Beatriz & Balbás, Raquel, 2017. "Differential equations connecting VaR and CVaR," IC3JM - Estudios = Working Papers 24017, Instituto Mixto Carlos III - Juan March de Ciencias Sociales (IC3JM).
    21. David B. Brown & Enrico De Giorgi & Melvyn Sim, 2012. "Aspirational Preferences and Their Representation by Risk Measures," Management Science, INFORMS, vol. 58(11), pages 2095-2113, November.
    22. Alejandro Balbás & Iván Blanco & José Garrido, 2014. "Measuring Risk When Expected Losses Are Unbounded," Risks, MDPI, vol. 2(4), pages 1-14, September.
    23. repec:cte:wbrepe:wb087114 is not listed on IDEAS
    24. Junhong Du & Zhiming Li & Lijun Wu, 2019. "Optimal Stop-Loss Reinsurance Under the VaR and CTE Risk Measures: Variable Transformation Method," Computational Economics, Springer;Society for Computational Economics, vol. 53(3), pages 1133-1151, March.
    25. Balbás, Alejandro & Balbás, Beatriz & Balbás, Raquel, 2010. "CAPM and APT-like models with risk measures," Journal of Banking & Finance, Elsevier, vol. 34(6), pages 1166-1174, June.

    More about this item

    Keywords

    VaR Optimization;

    JEL classification:

    • C02 - Mathematical and Quantitative Methods - - General - - - Mathematical Economics
    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions
    • G22 - Financial Economics - - Financial Institutions and Services - - - Insurance; Insurance Companies; Actuarial Studies

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:cte:imrepe:id-16-01. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Ana Poveda (email available below). General contact details of provider: http://www.march.es/ceacs/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.