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Stochastic optimization for allocation problems with shortfall risk constraints

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  • Roberto Casarin
  • Monica Billio

Abstract

One of the crucial aspects in asset allocation problems is the assumption concerning the probability distribution of asset returns. Financial managers generally suppose normal distribution, even if extreme realizations usually have an higher frequency than in the Gaussian case. The aim of this paper is to propose a general Monte Carlo simulation approach able to solve an asset allocation problem with shortfall constraint, and to evaluate the exact portfolio risk‐level when managers assume a misspecified return behaviour. We assume that returns are generated by a multivariate skewed Student‐t distribution where each marginal can have different degrees of freedom. The stochastic optimization allows us to value the effective risk for managers. In the empirical application we consider a symmetric and heterogeneous case, and interestingly note that a multivariate Student‐t with heterogeneous marginal distributions produces in the optimization problem a shortfall probability and a shortfall return level that can be adequately approximated by assuming a multivariate Student‐t with common degrees of freedom. Thus, the proposed simulation‐based approach could be an important instrument for investors who require a qualitative assessment of the reliability and sensitivity of their investment strategies in the case their models could be potentially misspecified. Copyright © 2007 John Wiley & Sons, Ltd.

Suggested Citation

  • Roberto Casarin & Monica Billio, 2007. "Stochastic optimization for allocation problems with shortfall risk constraints," Applied Stochastic Models in Business and Industry, John Wiley & Sons, vol. 23(3), pages 247-271, May.
  • Handle: RePEc:wly:apsmbi:v:23:y:2007:i:3:p:247-271
    DOI: 10.1002/asmb.671
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    Cited by:

    1. Maria Cristina Arcuri & Gino Gandolfi & Fabrizio Laurini, 2023. "Robust portfolio optimization for banking foundations: a CVaR approach for asset allocation with mandatory constraints," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 31(2), pages 557-581, June.
    2. Alessandro Fedele & Paolo M. Panteghini & Sergio Vergalli, 2011. "Optimal Investment and Financial Strategies under Tax‐Rate Uncertainty," German Economic Review, Verein für Socialpolitik, vol. 12(4), pages 438-468, November.
    3. Liu, Qingfu & Hua, Renhai & An, Yunbi, 2016. "Determinants and information content of intraday bid-ask spreads: Evidence from Chinese commodity futures markets," Pacific-Basin Finance Journal, Elsevier, vol. 38(C), pages 135-148.
    4. Del Boca, Alessandra & Fratianni, Michele & Spinelli, Franco & Trecroci, Carmine, 2010. "The Phillips curve and the Italian lira, 1861-1998," The North American Journal of Economics and Finance, Elsevier, vol. 21(2), pages 182-197, August.
    5. Marie Brière & Ombretta Signori, 2011. "Inflation hedging portfolios in different regimes," BIS Papers chapters, in: Bank for International Settlements (ed.), Portfolio and risk management for central banks and sovereign wealth funds, volume 58, pages 139-163, Bank for International Settlements.
    6. Amedeo Fossati & Rosella Levaggi, 2008. "Delay is not the answer: waiting time in health care & income redistribution," Working Papers 0801, University of Brescia, Department of Economics.
    7. Alessandro Fedele & Raffaele Miniaci, 2010. "Do Social Enterprises Finance Their Investments Differently from For-profit Firms? The Case of Social Residential Services in Italy," Journal of Social Entrepreneurship, Taylor & Francis Journals, vol. 1(2), pages 174-189, October.
    8. repec:dau:papers:123456789/9296 is not listed on IDEAS
    9. Martin Meier & Enrico Minelli & Herakles Polemarchakis, 2014. "Competitive markets with private information on both sides," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 55(2), pages 257-280, February.
    10. Luigi Grossi & Fabrizio Laurini, 2020. "Robust asset allocation with conditional value at risk using the forward search," Applied Stochastic Models in Business and Industry, John Wiley & Sons, vol. 36(3), pages 335-352, May.
    11. Rosella Levaggi & Francesco Menoncin, 2009. "Decentralized provision of merit and impure public goods," Working Papers 0909, University of Brescia, Department of Economics.
    12. Bisin, A. & Geanakoplos, J.D. & Gottardi, P. & Minelli, E. & Polemarchakis, H., 2011. "Markets and contracts," Journal of Mathematical Economics, Elsevier, vol. 47(3), pages 279-288.
    13. Francesco Menoncin & Paolo Panteghini, 2009. "Retrospective Capital Gains Taxation in the Real World," CESifo Working Paper Series 2674, CESifo.
    14. Alessandro Fedele & Francesco Liucci & Andrea Mantovani, 2009. "Credit availability in the crisis: the European investment bank group," Working Papers 0913, University of Brescia, Department of Economics.
    15. repec:dau:papers:123456789/7744 is not listed on IDEAS

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