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Comonotonic Approximations for Optimal Portfolio Selection Problems

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  • J. Dhaene
  • S. Vanduffel
  • M. J. Goovaerts
  • R. Kaas
  • D. Vyncke

Abstract

We investigate multiperiod portfolio selection problems in a Black and Scholes type market where a basket of 1 riskfree and "m" risky securities are traded continuously. We look for the optimal allocation of wealth within the class of "constant mix" portfolios. First, we consider the portfolio selection problem of a decision maker who invests money at predetermined points in time in order to obtain a target capital at the end of the time period under consideration. A second problem concerns a decision maker who invests some amount of money (the initial wealth or provision) in order to be able to fullfil a series of future consumptions or payment obligations. Several optimality criteria and their interpretation within Yaari's dual theory of choice under risk are presented. For both selection problems, we propose accurate approximations based on the concept of comonotonicity, as studied in Dhaene et al. (2002 a,b). Our analytical approach avoids simulation, and hence reduces the computing effort drastically. Copyright The Journal of Risk and Insurance.

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Bibliographic Info

Article provided by The American Risk and Insurance Association in its journal The Journal of Risk and Insurance.

Volume (Year): 72 (2005)
Issue (Month): 2 ()
Pages: 253-300

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Handle: RePEc:bla:jrinsu:v:72:y:2005:i:2:p:253-300

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Cited by:
  1. Erhan Bayraktar & Virginia R. Young, 2007. "Minimizing the Probability of Lifetime Ruin under Borrowing Constraints," Papers math/0703850, arXiv.org.
  2. Fr\'ed\'eric Planchet & Pierre-Emanuel Th\'erond, 2010. "Allocation d'actifs selon le crit\`ere de maximisation des fonds propres \'economiques en assurance non-vie," Papers 1001.1867, arXiv.org.
  3. de Jong, Frank, 2008. "Pension fund investments and the valuation of liabilities under conditional indexation," Insurance: Mathematics and Economics, Elsevier, vol. 42(1), pages 1-13, February.
  4. Frédéric Planchet & Pierre-Emmanuel Thérond, 2007. "Allocation d'actifs selon le critère de maximisation des fonds propres économiques en assurance non-vie : présentation et mise en oeuvre dans la réglementation française et dans un référentiel ," Post-Print hal-00443028, HAL.
  5. Leung, Andrew P., 2011. "Reactive investment strategies," Insurance: Mathematics and Economics, Elsevier, vol. 49(1), pages 89-99, July.
  6. Dhaene, Jan & Goovaerts, Marc & Vanmaele, Michèle & Van Weert, Koen, 2012. "Convex order approximations in the case of cash flows of mixed signs," Insurance: Mathematics and Economics, Elsevier, vol. 51(2), pages 249-256.
  7. 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.
  8. Bakken, Henrik & Lindset, Snorre & Olson, Lars Hesstvedt, 2006. "Pricing of multi-period rate of return guarantees: The Monte Carlo approach," Insurance: Mathematics and Economics, Elsevier, vol. 39(1), pages 135-149, August.
  9. Bauerle, Nicole & Muller, Alfred, 2006. "Stochastic orders and risk measures: Consistency and bounds," Insurance: Mathematics and Economics, Elsevier, vol. 38(1), pages 132-148, February.
  10. Carry Mout, 2006. "An Upper Bound of the Sum of Risks: two Applications of Comonotonicity," DNB Working Papers 105, Netherlands Central Bank, Research Department.
  11. 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.
  12. Van Weert, Koen & Dhaene, Jan & Goovaerts, Marc, 2010. "Optimal portfolio selection for general provisioning and terminal wealth problems," Insurance: Mathematics and Economics, Elsevier, vol. 47(1), pages 90-97, August.
  13. Pagnoncelli, Bernardo K. & Vanduffel, Steven, 2012. "A provisioning problem with stochastic payments," European Journal of Operational Research, Elsevier, vol. 221(2), pages 445-453.
  14. Cheung, Ka Chun, 2006. "Optimal portfolio problem with unknown dependency structure," Insurance: Mathematics and Economics, Elsevier, vol. 38(1), pages 167-175, February.

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