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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.

Suggested Citation

  • 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.
    • Handle: RePEc:bla:jrinsu:v:72:y:2005:i:2:p:253-300
    DOI: 10.1111/j.1539-6975.2005.00123.x
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    References listed on IDEAS

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    1. J. Dhaene & S. Vanduffel & M. Goovaerts, 2007. "Comonotonicity," Review of Business and Economic Literature, KU Leuven, Faculty of Economics and Business (FEB), Review of Business and Economic Literature, vol. 0(2), pages 265-278.
    2. 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.
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