Comonotonic Approximations for Optimal Portfolio Selection Problems

Journal of Risk and Insurance, Vol. 72, No. 2, pp. 253-301, 2005

45 Pages Posted: 19 May 2009  

Jan Dhaene

Katholieke Universiteit Leuven - Faculty of Economics and Business

Steven Vanduffel

Vrije Universiteit Brussel (VUB)

M. J. Goovaerts

affiliation not provided to SSRN

Rob Kaas

University of Amsterdam - Faculty of Economics & Econometrics (FEE)

David Vyncke

Ghent University-Universiteit Gent - Department of Applied Mathematics and Computer Science

Date Written: 2005

Abstract

We investigate multiperiod portfolio selection problems in a Black & 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, Denuit, Goovaerts, Kaas & Vyncke (2002 a,b). Our analytical approach avoids simulation, and hence reduces the computing effort drastically.

Keywords: Optimal Portfolio selection, Comonotonicity, asset allocation, Merton, constant mix

Suggested Citation

Dhaene, Jan and Vanduffel, Steven and Goovaerts, M. J. and Kaas, Rob and Vyncke, David, Comonotonic Approximations for Optimal Portfolio Selection Problems (2005). Journal of Risk and Insurance, Vol. 72, No. 2, pp. 253-301, 2005. Available at SSRN: https://ssrn.com/abstract=1406884

Jan Dhaene

Katholieke Universiteit Leuven - Faculty of Economics and Business ( email )

Naamsestraat 69
Leuven, 3000
Belgium

Steven Vanduffel (Contact Author)

Vrije Universiteit Brussel (VUB) ( email )

Pleinlaan 2
Brussels, Brabant 1050
Belgium

HOME PAGE: http://www.stevenvanduffel.com

M.J. Goovaerts

affiliation not provided to SSRN

Rob Kaas

University of Amsterdam - Faculty of Economics & Econometrics (FEE) ( email )

Roetersstraat 11
Amsterdam, 1018 WB
Netherlands

David Vyncke

Ghent University-Universiteit Gent - Department of Applied Mathematics and Computer Science ( email )

Gent, 9000
Belgium

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