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Background Risk Models and Stepwise Portfolio Construction

Author

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  • Alexandru V. Asimit

    (City University)

  • Raluca Vernic

    (Ovidius University of Constanta
    Institute of Mathematical Statistics and Applied Mathematics)

  • Ricardas Zitikis

    (University of Western Ontario)

Abstract

Assuming the multiplicative background risk model, which has been a popular model due to its practical applicability and technical tractability, we develop a general framework for analyzing portfolio performance based on its subportfolios. Since the performance of subportfolios is easier to assess, the herein developed stepwise portfolio construction (SPC) provides a powerful alternative to a number of traditional portfolio construction methods. Within this framework, we discuss a number of multivariate risk models that appear in the actuarial and financial literature. We provide numerical and graphical examples that illustrate the SPC technique and facilitate our understanding of the herein developed general results.

Suggested Citation

  • Alexandru V. Asimit & Raluca Vernic & Ricardas Zitikis, 2016. "Background Risk Models and Stepwise Portfolio Construction," Methodology and Computing in Applied Probability, Springer, vol. 18(3), pages 805-827, September.
    • Handle: RePEc:spr:metcap:v:18:y:2016:i:3:d:10.1007_s11009-015-9458-3
    DOI: 10.1007/s11009-015-9458-3
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    1. Buch, Arne & Dorfleitner, Gregor & Wimmer, Maximilian, 2011. "Risk capital allocation for RORAC optimization," Journal of Banking & Finance, Elsevier, vol. 35(11), pages 3001-3009, November.
    2. Michaud, Richard O. & Michaud, Robert O., 2008. "Efficient Asset Management: A Practical Guide to Stock Portfolio Optimization and Asset Allocation," OUP Catalogue, Oxford University Press, edition 2, number 9780195331912.
    3. Marc Busse & Michel Dacorogna & Marie Kratz, 2014. "The Impact of Systemic Risk on the Diversification Benefits of a Risk Portfolio," Risks, MDPI, vol. 2(3), pages 1-17, July.
    4. Franke, Guenter & Schlesinger, Harris & Stapleton, Richard C., 2011. "Risk taking with additive and multiplicative background risks," Journal of Economic Theory, Elsevier, vol. 146(4), pages 1547-1568, July.
    5. Guillén, Montserrat & Sarabia, José María & Prieto, Faustino, 2013. "Simple risk measure calculations for sums of positive random variables," Insurance: Mathematics and Economics, Elsevier, vol. 53(1), pages 273-280.
    6. Yau, Sheena & Kwon, Roy H. & Scott Rogers, J. & Wu, Desheng, 2011. "Financial and operational decisions in the electricity sector: Contract portfolio optimization with the conditional value-at-risk criterion," International Journal of Production Economics, Elsevier, vol. 134(1), pages 67-77, November.
    7. Raluca Vernic, 2011. "Tail Conditional Expectation for the Multivariate Pareto Distribution of the Second Kind: Another Approach," Methodology and Computing in Applied Probability, Springer, vol. 13(1), pages 121-137, March.
    8. Enkelejd Hashorva & Lanpeng Ji, 2014. "Random Shifting and Scaling of Insurance Risks," Risks, MDPI, vol. 2(3), pages 1-12, July.
    9. Mainik, Georg & Embrechts, Paul, 2013. "Diversification in heavy-tailed portfolios: properties and pitfalls," Annals of Actuarial Science, Cambridge University Press, vol. 7(1), pages 26-45, March.
    10. Ilia Tsetlin & Robert L. Winkler, 2005. "Risky Choices and Correlated Background Risk," Management Science, INFORMS, vol. 51(9), pages 1336-1345, September.
    11. Tsanakas, Andreas, 2008. "Risk measurement in the presence of background risk," Insurance: Mathematics and Economics, Elsevier, vol. 42(2), pages 520-528, April.
    12. Hristo S. Sendov & Ričardas Zitikis, 2014. "The Shape of the Borwein–Affleck–Girgensohn Function Generated by Completely Monotone and Bernstein Functions," Journal of Optimization Theory and Applications, Springer, vol. 160(1), pages 67-89, January.
    13. Marasovic, Branka & Babic, Zoran, 2011. "Two-step multi-criteria model for selecting optimal portfolio," International Journal of Production Economics, Elsevier, vol. 134(1), pages 58-66, November.
    14. McNeil, Alexander J., 2013. "Enterprise Risk Management," Annals of Actuarial Science, Cambridge University Press, vol. 7(01), pages 1-2, March.
    15. Embrechts, Paul & Puccetti, Giovanni & Rüschendorf, Ludger, 2013. "Model uncertainty and VaR aggregation," Journal of Banking & Finance, Elsevier, vol. 37(8), pages 2750-2764.
    16. Edward Furman & Ričardas Zitikis, 2009. "Weighted Pricing Functionals With Applications to Insurance," North American Actuarial Journal, Taylor & Francis Journals, vol. 13(4), pages 483-496.
    17. Zhidong Bai & Yongchang Hui & Wing-Keung Wong & Ričardas Zitikis, 2012. "Prospect Performance Evaluation: Making a Case for a Non-asymptotic UMPU Test," Journal of Financial Econometrics, Oxford University Press, vol. 10(4), pages 703-732, September.
    18. Günter Franke & Harris Schlesinger & Richard C. Stapleton, 2006. "Multiplicative Background Risk," Management Science, INFORMS, vol. 52(1), pages 146-153, January.
    19. Brazauskas, Vytaras & Jones, Bruce L. & Zitikis, RiÄ ardas, 2015. "Trends in disguise," Annals of Actuarial Science, Cambridge University Press, vol. 9(1), pages 58-71, March.
    20. Asimit, Alexandru V. & Furman, Edward & Tang, Qihe & Vernic, Raluca, 2011. "Asymptotics for risk capital allocations based on Conditional Tail Expectation," Insurance: Mathematics and Economics, Elsevier, vol. 49(3), pages 310-324.
    21. Mark Bebbington & Chin‐Diew Lai & Ričardas Zitikis, 2008. "Reduction in mean residual life in the presence of a constant competing risk," Applied Stochastic Models in Business and Industry, John Wiley & Sons, vol. 24(1), pages 51-63, January.
    22. Michael Merz & Mario V. Wüthrich, 2014. "Demand of Insurance under the Cost-of-Capital Premium Calculation Principle," Risks, MDPI, vol. 2(2), pages 1-23, June.
    23. David Stefanovits & Urs Schubiger & Mario V. Wüthrich, 2014. "Model Risk in Portfolio Optimization," Risks, MDPI, vol. 2(3), pages 1-34, August.
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    Cited by:

    1. Martín Egozcue & Jiang Wu & Ričardas Zitikis, 2017. "Optimal two-stage pricing strategies from the seller’s perspective under the uncertainty of buyer’s decisions," Journal of Statistical Distributions and Applications, Springer, vol. 4(1), pages 1-25, December.
    2. N. V. Gribkova & J. Su & R. Zitikis, 2022. "Empirical tail conditional allocation and its consistency under minimal assumptions," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 74(4), pages 713-735, August.
    3. Eric C. K. Cheung & Oscar Peralta & Jae-Kyung Woo, 2021. "Multivariate matrix-exponential affine mixtures and their applications in risk theory," Papers 2201.11122, arXiv.org.
    4. Jianxi Su & Edward Furman, 2016. "A form of multivariate Pareto distribution with applications to financial risk measurement," Papers 1607.04737, arXiv.org.
    5. Claude Lefèvre & Stéphane Loisel & Pierre Montesinos, 2020. "Bounding Basis-Risk Using s-convex Orders on Beta-unimodal Distributions," Post-Print hal-02611227, HAL.
    6. Vadim Semenikhine & Edward Furman & Jianxi Su, 2018. "On a Multiplicative Multivariate Gamma Distribution with Applications in Insurance," Risks, MDPI, vol. 6(3), pages 1-20, August.
    7. Jiang Wu & Ricardas Zitikis, 2016. "Should we opt for the Black Friday discounted price or wait until the Boxing Day?," Papers 1612.05855, arXiv.org.
    8. Mercè Claramunt, M. & Lefèvre, Claude & Loisel, Stéphane & Montesinos, Pierre, 2022. "Basis risk management and randomly scaled uncertainty," Insurance: Mathematics and Economics, Elsevier, vol. 107(C), pages 123-139.
    9. Su, Jianxi & Hua, Lei, 2017. "A general approach to full-range tail dependence copulas," Insurance: Mathematics and Economics, Elsevier, vol. 77(C), pages 49-64.
    10. Gribkova, N.V. & Su, J. & Zitikis, R., 2022. "Inference for the tail conditional allocation: Large sample properties, insurance risk assessment, and compound sums of concomitants," Insurance: Mathematics and Economics, Elsevier, vol. 107(C), pages 199-222.
    11. Furman, Edward & Kye, Yisub & Su, Jianxi, 2021. "Multiplicative background risk models: Setting a course for the idiosyncratic risk factors distributed phase-type," Insurance: Mathematics and Economics, Elsevier, vol. 96(C), pages 153-167.
    12. Cheung, Eric C.K. & Peralta, Oscar & Woo, Jae-Kyung, 2022. "Multivariate matrix-exponential affine mixtures and their applications in risk theory," Insurance: Mathematics and Economics, Elsevier, vol. 106(C), pages 364-389.
    13. Indranil Ghosh, 2018. "A complete characterization of bivariate densities using the conditional percentile function," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 81(5), pages 485-492, July.

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