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Spektrale Risikomaße: Konzeption, betriebswirtschaftliche Anwendungen und Fallstricke

Listed author(s):
  • Mario Brandtner

    ()

    (Friedrich-Schiller-Universität Jena)

Registered author(s):

    Zusammenfassung Der Beitrag behandelt Probleme und Anwendungspotenziale bei der Übertragung der originär regulatorisch geprägten spektralen Risikomaße, einschließlich des Conditional Value-at-Risk als ihrem prominentesten Vertreter, in den Kontext betriebswirtschaftlicher Entscheidungsprobleme. Dabei werden zwei Grundformen von restriktiven, und ökonomisch unplausiblen, Randlösungstendenzen oder ,,Plunging“ offengelegt. Die erste Form von Randlösungen wird unmittelbar durch die regulatorische Axiomatik induziert und ist allen spektralen Risikomaßen inhärent. Sie bewirkt etwa, dass bei der optimalen Vermögensaufteilung zwischen einer risikofreien und einer riskanten Anlage niemals diversifiziert wird. Eine zweite Form von Randlösungen geht auf das spezielle Risikospektrum des Conditional Value-at-Risk zurück. Im Kontext optimaler Versicherungsentscheidungen mittels stop-loss-Kontrakt führt dieses dazu, dass die Versicherung bei Verwendung spektraler Risikomaße als Zielfunktion entweder gar nicht oder nur zum minimalen Selbstbehalt abgeschlossen wird. Ähnliche Schwächen finden sich auch in anderen Anwendungen, etwa bei der der Ermittlung optimaler Bestellmengen im Newsvendor-Modell. Wir können zeigen, dass diese zweite Form von Randlösungstendenzen bereits innerhalb der Klasse der spektralen Risikomaße, etwa durch die Anwendung der Subklasse der power spektralen Risikomaße anstelle des Conditional Value-at-Risk, behoben werden kann.

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    File URL: http://link.springer.com/10.1007/s11301-015-0116-1
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    Article provided by Springer & Vienna University of Economics and Business in its journal Management Review Quarterly.

    Volume (Year): 66 (2016)
    Issue (Month): 2 (April)
    Pages: 75-115

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    Handle: RePEc:spr:manrev:v:66:y:2016:i:2:d:10.1007_s11301-015-0116-1
    DOI: 10.1007/s11301-015-0116-1
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    1. Frittelli, Marco & Rosazza Gianin, Emanuela, 2002. "Putting order in risk measures," Journal of Banking & Finance, Elsevier, vol. 26(7), pages 1473-1486, July.
    2. Gordon J. Alexander & Alexandre M. Baptista, 2004. "A Comparison of VaR and CVaR Constraints on Portfolio Selection with the Mean-Variance Model," Management Science, INFORMS, vol. 50(9), pages 1261-1273, September.
    3. Gilbert W. Bassett, 2004. "Pessimistic Portfolio Allocation and Choquet Expected Utility," Journal of Financial Econometrics, Society for Financial Econometrics, vol. 2(4), pages 477-492.
    4. Khouja, Moutaz, 1999. "The single-period (news-vendor) problem: literature review and suggestions for future research," Omega, Elsevier, vol. 27(5), pages 537-553, October.
    5. Sarin, Rakesh K. & Weber, Martin, 1993. "Risk-value models," European Journal of Operational Research, Elsevier, vol. 70(2), pages 135-149, October.
    6. Yamai, Yasuhiro & Yoshiba, Toshinao, 2002. "Comparative Analyses of Expected Shortfall and Value-at-Risk: Their Estimation Error, Decomposition, and Optimization," Monetary and Economic Studies, Institute for Monetary and Economic Studies, Bank of Japan, vol. 20(1), pages 87-121, January.
    7. Yaari, Menahem E, 1987. "The Dual Theory of Choice under Risk," Econometrica, Econometric Society, vol. 55(1), pages 95-115, January.
    8. Szego, Giorgio, 2002. "Measures of risk," Journal of Banking & Finance, Elsevier, vol. 26(7), pages 1253-1272, July.
    9. Jammernegg, Werner & Kischka, Peter, 2009. "Risk preferences and robust inventory decisions," International Journal of Production Economics, Elsevier, vol. 118(1), pages 269-274, March.
    10. Doherty, Neil A & Eeckhoudt, Louis, 1995. "Optimal Insurance without Expected Utility: The Dual Theory and the Linearity of Insurance Contracts," Journal of Risk and Uncertainty, Springer, vol. 10(2), pages 157-179, March.
    11. Eeckhoudt, Louis & Gollier, Christian & Schlesinger, Harris, 1991. "Increases in risk and deductible insurance," Journal of Economic Theory, Elsevier, vol. 55(2), pages 435-440, December.
    12. Kevin Dowd & John Cotter & Ghulam Sorwar, 2008. "Spectral Risk Measures: Properties and Limitations," Journal of Financial Services Research, Springer;Western Finance Association, vol. 34(1), pages 61-75, August.
    13. Yamai, Yasuhiro & Yoshiba, Toshinao, 2005. "Value-at-risk versus expected shortfall: A practical perspective," Journal of Banking & Finance, Elsevier, vol. 29(4), pages 997-1015, April.
    14. Cotter, John & Dowd, Kevin, 2006. "Extreme spectral risk measures: An application to futures clearinghouse margin requirements," Journal of Banking & Finance, Elsevier, vol. 30(12), pages 3469-3485, December.
    15. Alexander, Gordon J. & Baptista, Alexandre M., 2002. "Economic implications of using a mean-VaR model for portfolio selection: A comparison with mean-variance analysis," Journal of Economic Dynamics and Control, Elsevier, vol. 26(7-8), pages 1159-1193, July.
    16. Adam, Alexandre & Houkari, Mohamed & Laurent, Jean-Paul, 2008. "Spectral risk measures and portfolio selection," Journal of Banking & Finance, Elsevier, vol. 32(9), pages 1870-1882, September.
    17. J. Tobin, 1958. "Liquidity Preference as Behavior Towards Risk," Review of Economic Studies, Oxford University Press, vol. 25(2), pages 65-86.
    18. Benati, Stefano, 2003. "The optimal portfolio problem with coherent risk measure constraints," European Journal of Operational Research, Elsevier, vol. 150(3), pages 572-584, November.
    19. Gotoh, Jun-ya & Takano, Yuichi, 2007. "Newsvendor solutions via conditional value-at-risk minimization," European Journal of Operational Research, Elsevier, vol. 179(1), pages 80-96, May.
    20. Christian Gollier & Harris Schlesinger, 1996. "Arrow's theorem on the optimality of deductibles: A stochastic dominance approach (*)," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 7(2), pages 359-363.
    21. Kai A. Konrad & Stergios Skaperdas, 1993. "Self-Insurance and Self-Protection: A Nonexpected Utility Analysis," The Geneva Risk and Insurance Review, Palgrave Macmillan;International Association for the Study of Insurance Economics (The Geneva Association), vol. 18(2), pages 131-146, December.
    22. Tasche, Dirk, 2002. "Expected shortfall and beyond," Journal of Banking & Finance, Elsevier, vol. 26(7), pages 1519-1533, July.
    23. Hadar, Josef & Russell, William R, 1969. "Rules for Ordering Uncertain Prospects," American Economic Review, American Economic Association, vol. 59(1), pages 25-34, March.
    24. Acerbi Carlo & Simonetti Prospero, 2002. "Portfolio Optimization with Spectral Measures of Risk," Papers cond-mat/0203607, arXiv.org.
    25. Marcin Fałdziński & Magdalena Osińska & Tomasz Zdanowicz, 2012. "Detecting Risk Transfer in Financial Markets using Different Risk Measures," Central European Journal of Economic Modelling and Econometrics, CEJEME, vol. 4(1), pages 45-64, March.
    26. Wang, Shaun S. & Young, Virginia R. & Panjer, Harry H., 1997. "Axiomatic characterization of insurance prices," Insurance: Mathematics and Economics, Elsevier, vol. 21(2), pages 173-183, November.
    27. Massimiliano Barbi & Silvia Romagnoli, 2016. "Optimal hedge ratio under a subjective re-weighting of the original measure," Applied Economics, Taylor & Francis Journals, vol. 48(14), pages 1271-1280, March.
    28. A. Cherny, 2006. "Weighted V@R and its Properties," Finance and Stochastics, Springer, vol. 10(3), pages 367-393, September.
    29. John Cotter & Kevin Dowd, 2010. "Estimating financial risk measures for futures positions: A nonparametric approach," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 30(7), pages 689-703, 07.
    30. Wächter, Hans Peter & Mazzoni, Thomas, 2013. "Consistent modeling of risk averse behavior with spectral risk measures," European Journal of Operational Research, Elsevier, vol. 229(2), pages 487-495.
    31. Kevin Dowd & David Blake, 2006. "After VaR: The Theory, Estimation, and Insurance Applications of Quantile-Based Risk Measures," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 73(2), pages 193-229.
    32. Werner Jammernegg & Peter Kischka, 2007. "Risk-averse and risk-taking newsvendors: a conditional expected value approach," Review of Managerial Science, Springer, vol. 1(1), pages 93-110, April.
    33. Acerbi, Carlo, 2002. "Spectral measures of risk: A coherent representation of subjective risk aversion," Journal of Banking & Finance, Elsevier, vol. 26(7), pages 1505-1518, July.
    34. Acerbi, Carlo & Tasche, Dirk, 2002. "On the coherence of expected shortfall," Journal of Banking & Finance, Elsevier, vol. 26(7), pages 1487-1503, July.
    35. Cai, Jun & Tan, Ken Seng & Weng, Chengguo & Zhang, Yi, 2008. "Optimal reinsurance under VaR and CTE risk measures," Insurance: Mathematics and Economics, Elsevier, vol. 43(1), pages 185-196, August.
    36. Brandtner, Mario & Kürsten, Wolfgang, 2014. "Solvency II, regulatory capital, and optimal reinsurance: How good are Conditional Value-at-Risk and spectral risk measures?," Insurance: Mathematics and Economics, Elsevier, vol. 59(C), pages 156-167.
    37. Johannes Leitner, 2005. "A Short Note On Second-Order Stochastic Dominance Preserving Coherent Risk Measures," Mathematical Finance, Wiley Blackwell, vol. 15(4), pages 649-651.
    38. Tan, Ken Seng & Weng, Chengguo & Zhang, Yi, 2011. "Optimality of general reinsurance contracts under CTE risk measure," Insurance: Mathematics and Economics, Elsevier, vol. 49(2), pages 175-187, September.
    39. Ross, Stephen A, 1981. "Some Stronger Measures of Risk Aversion in the Small and the Large with Applications," Econometrica, Econometric Society, vol. 49(3), pages 621-638, May.
    40. Cui, Wei & Yang, Jingping & Wu, Lan, 2013. "Optimal reinsurance minimizing the distortion risk measure under general reinsurance premium principles," Insurance: Mathematics and Economics, Elsevier, vol. 53(1), pages 74-85.
    41. Alexander, Gordon J. & Baptista, Alexandre M., 2006. "Does the Basle Capital Accord reduce bank fragility? An assessment of the value-at-risk approach," Journal of Monetary Economics, Elsevier, vol. 53(7), pages 1631-1660, October.
    42. Cai, Jun & Tan, Ken Seng, 2007. "Optimal Retention for a Stop-loss Reinsurance Under the VaR and CTE Risk Measures," ASTIN Bulletin: The Journal of the International Actuarial Association, Cambridge University Press, vol. 37(01), pages 93-112, May.
    43. Philippe Artzner & Freddy Delbaen & Jean-Marc Eber & David Heath, 1999. "Coherent Measures of Risk," Mathematical Finance, Wiley Blackwell, vol. 9(3), pages 203-228.
    44. Rothschild, Michael & Stiglitz, Joseph E., 1970. "Increasing risk: I. A definition," Journal of Economic Theory, Elsevier, vol. 2(3), pages 225-243, September.
    45. David Heath & Hyejin Ku, 2004. "Pareto Equilibria with coherent measures of risk," Mathematical Finance, Wiley Blackwell, vol. 14(2), pages 163-172.
    46. Cass, David & Stiglitz, Joseph E., 1970. "The structure of investor preferences and asset returns, and separability in portfolio allocation: A contribution to the pure theory of mutual funds," Journal of Economic Theory, Elsevier, vol. 2(2), pages 122-160, June.
    47. Chi, Yichun & Tan, Ken Seng, 2011. "Optimal Reinsurance under VaR and CVaR Risk Measures: a Simplified Approach," ASTIN Bulletin: The Journal of the International Actuarial Association, Cambridge University Press, vol. 41(02), pages 487-509, November.
    48. Mark J. Machina, 1995. "Non-Expected Utility and The Robustness of the Classical Insurance Paradigm," The Geneva Risk and Insurance Review, Palgrave Macmillan;International Association for the Study of Insurance Economics (The Geneva Association), vol. 20(1), pages 9-50, June.
    49. Rockafellar, R. Tyrrell & Uryasev, Stanislav, 2002. "Conditional value-at-risk for general loss distributions," Journal of Banking & Finance, Elsevier, vol. 26(7), pages 1443-1471, July.
    50. Brandtner, Mario, 2013. "Conditional Value-at-Risk, spectral risk measures and (non-)diversification in portfolio selection problems – A comparison with mean–variance analysis," Journal of Banking & Finance, Elsevier, vol. 37(12), pages 5526-5537.
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