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Stochastic Optimisation for Allocation Problems with Shortfall Risk Constraints


  • Roberto Casarin
  • Monica Billio


One of the most important 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 in order to solve an asset allocation problem with shortfall constraint, and to evaluate the exact portfolio risk-level when managers assume a misspecified tails behaviour. In this work we assume, as an example, that returns are generated by a multivariate Student-t distribution, while in reality returns come from a multivariate skewed Student-t distribution where each marginal has different degrees of freedom. Stochastic optimisation allows us to value the effective risk for managers. In the specific case analysed, it is also interesting to observe that a multivariate Student-t with heterogeneous marginal distributions produces a shortfall probability and a shortfall return level that can be approximated adequately by assuming a multivariate Student-t with a common degree of freedom in the optimisation problem. The present simulation based approach could be an important instrument for investors who need a qualitative assessment of the reliability and sensitivity of their investment strategies when their models are potentially misspecified.

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  • Roberto Casarin & Monica Billio, 2006. "Stochastic Optimisation for Allocation Problems with Shortfall Risk Constraints," Working Papers ubs0618, University of Brescia, Department of Economics.
  • Handle: RePEc:ubs:wpaper:ubs0618

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    1. Tavelli, Henry & Tullio, Giuseppe & Spinelli, Franco, 1998. "The Evolution of European Central Bank Independence: An Updating of the Masciandaro and Spinelli Index," Scottish Journal of Political Economy, Scottish Economic Society, vol. 45(3), pages 341-344, August.
    2. Fratianni,Michele & Spinelli,Franco, 2005. "A Monetary History of Italy," Cambridge Books, Cambridge University Press, number 9780521023450, March.
    3. DETKEN Carsten & SMETS Frank, "undated". "Asset Price Booms and Monetary Policy," EcoMod2003 330700042, EcoMod.
    4. Claudio E. V. Borio & Philip Lowe, 2004. "Securing sustainable price stability: should credit come back from the wilderness?," BIS Working Papers 157, Bank for International Settlements.
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    Cited by:

    1. 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.
    2. Rosella Levaggi & Francesco Menoncin, 2009. "Decentralized provision of merit and impure public goods," Working Papers 0909, University of Brescia, Department of Economics.
    3. 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.
    4. Francesco Menoncin & Paolo Panteghini, 2009. "Retrospective Capital Gains Taxation in the Real World," CESifo Working Paper Series 2674, CESifo Group Munich.
    5. 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.
    6. 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.
    7. 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.
    8. 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.
    9. 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.
    10. 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.
    11. repec:dau:papers:123456789/9296 is not listed on IDEAS
    12. repec:dau:papers:123456789/7744 is not listed on IDEAS

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