Chance-constrained portfolio selection is an approach to
portfolio selection under
loss aversion.
The formulation assumes that (i) investor's preferences are representable by the
expected utility of final wealth, and that (ii) they require that the probability of their final wealth falling below a
survival or safety level must to be acceptably low.
The chance-constrained portfolio problem is then to find:
Max wjE(Xj), subject to Pr( wjXj < s) ≤ α, wj = 1, wj ≥ 0 for all j,
where s is the survival level and α is the admissible
probability of ruin; w is the weight and x is the value of the jth asset to be included in the portfolio.
For fixed α the chance-constrained portfolio problem represents
lexicographic preferences and is an implementation of
capital asset pricing under loss aversion.
In general though, it is observed[4] that no
utility function can represent the preference ordering of chance-constrained programming because a fixed α does not admit compensation for a small increase in α by any increase in expected wealth.
^A. Chance and W. W. Cooper (1959), "Chance-Constrained Programming," Management Science, 6, No. 1, 73-79.
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[2] Retrieved September 24, 2020.
^Agnew, N.H, R.A. Agnes, J. Rasmussen and K. R. Smith (1969), "An Application of Chance-Constrained Programming to Portfolio Selection in a Casualty Insurance Firm," Management Science, 15, No. 10, 512-520.
[3]. Retrieved September 24, 2020.
^Borch, K. H. (1968), The Economics of Uncertainty, Princeton University Press, Princeton.
[4]. Retrieved September 24, 2020.
^Seppälä, J. (1994), “The diversification of currency loans: A comparison between safety-first and mean-variance criteria,” European Journal of Operations Research, 74, 325-343.
[5]. Retrieved September 25, 2020.
^Bay, X., X. Zheng and X. Sun (2012), "A survey on probabilistic constrained optimization problems," Numerical Algebra, Control and Optimization, 2, No. 4, 767-778.
[6]. Retrieved September 25, 2020.
^Pyle, D. H. and
Stephen J. Turnovsky (1971), “Risk Aversion in Chance Constrained Portfolio Selection, Management Science,18, No. 3, 218-225.
[7]. Retrieved September 24, 2020.