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Comparing Approximations for Risk Measures of Sums of Nonindependent Lognormal Random Variables

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  • Steven Vanduffel
  • Tom Hoedemakers
  • Jan Dhaene

Abstract

In this paper we consider different approximations for computing the distribution function or risk measures related to a discrete sum of nonindependent lognormal random variables. Comonotonic upper and lower bound approximations for such sums have been proposed in Dhaene et al. (2002a,b). We introduce the comonotonic “maximal variance” lower bound approximation. We also compare the comonotonic approximations with two well-known moment-matching approximations: the lognormal and the reciprocal Gamma approximations. We find that for a wide range of parameter values the comonotonic “maximal variance” lower bound approximation outperforms the other approximations.

Suggested Citation

  • Steven Vanduffel & Tom Hoedemakers & Jan Dhaene, 2005. "Comparing Approximations for Risk Measures of Sums of Nonindependent Lognormal Random Variables," North American Actuarial Journal, Taylor & Francis Journals, vol. 9(4), pages 71-82.
    • Handle: RePEc:taf:uaajxx:v:9:y:2005:i:4:p:71-82
    DOI: 10.1080/10920277.2005.10596226
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    Cited by:

    1. Timofeeva, Anastasiia, 2015. "On endogeneity of consumer expenditures in the estimation of households demand system," Applied Econometrics, Russian Presidential Academy of National Economy and Public Administration (RANEPA), vol. 37(1), pages 87-106.
    2. Peter Løchte Jørgensen, 2007. "Lognormal Approximation of Complex Path-Dependent Pension Scheme Payoffs," The European Journal of Finance, Taylor & Francis Journals, vol. 13(7), pages 595-619.
    3. J. Marin-Solano (Universitat de Barcelona) & O. Roch (Universitat de Barcelona) & J. Dhaene (Katholieke Univerisiteit Leuven) & C. Ribas (Universitat de Barcelona) & M. Bosch-Princep (Universitat de B, 2009. "Buy-and-Hold Strategies and Comonotonic Approximations," Working Papers in Economics 213, Universitat de Barcelona. Espai de Recerca en Economia.
    4. Zadourian, Rubina & Klümper, Andreas, 2018. "Exact probability distribution function for the volatility of cumulative production," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 495(C), pages 59-66.
    5. DE SCHEPPER, Ann & HEIJNEN, Bart, 2006. "Risk management under incomplete information: Exact upper and lower bounds for the Value at Risk," Working Papers 2006020, University of Antwerp, Faculty of Business and Economics.
    6. J. Dhaene & S. Vanduffel & M. J. Goovaerts & R. Kaas & D. Vyncke, 2005. "Comonotonic Approximations for Optimal Portfolio Selection Problems," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 72(2), pages 253-300, June.

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