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Comonotonic Approximations for Optimal Portfolio Selection Problems

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Author Info
J. Dhaene
S. Vanduffel
M. J. Goovaerts
R. Kaas
D. Vyncke

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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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File URL: http://www.blackwell-synergy.com/doi/abs/10.1111/j.1539-6975.2005.00123.x
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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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  1. Erhan Bayraktar & Virginia R. Young, 2007. "Minimizing the Probability of Lifetime Ruin under Borrowing Constraints," Quantitative Finance Papers math/0703850, arXiv.org. [Downloadable!]
  2. Carry Mout, 2006. "An Upper Bound of the Sum of Risks: two Applications of Comonotonicity," DNB Working Papers 105, Netherlands Central Bank, Research Department. [Downloadable!]
  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. [Downloadable!]
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