Chance-constrained portfolio selection

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

\sum _{j}

w_jE(X_j), subject to Pr(

\sum _{j}

w_jX_j < s) ≤

α

,

\sum _{j}

w_j = 1, w_j ≥ 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.

The original implementation is based on the seminal work of Abraham Charnes and William W. Cooper on chance constrained programming in 1959,^[1] and was first applied to finance by Bertil Naslund and Andrew B. Whinston in 1962^[2] and in 1969 by N. H. Agnew, et al.^[3]

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.

For a comparison to mean-variance and safety-first portfolio problems, see;^[5] for a survey of solution methods here, see;^[6] for a discussion of the risk aversion properties of chance-constrained portfolio selection, see.^[7]

References

^ A. Chance and W. W. Cooper (1959), "Chance-Constrained Programming," Management Science, 6, No. 1, 73-79. [1]. Retrieved September 24, 2020
^ Naslund, B. and A. Whinston (1962), "A Model of Multi-Period Investment under Uncertainty," Management Science, 8, No. 2, 184-200. [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.

[1] A. Chance and W. W. Cooper (1959), "Chance-Constrained Programming," Management Science, 6, No. 1, 73-79. [1]. Retrieved September 24, 2020

[2] Naslund, B. and A. Whinston (1962), "A Model of Multi-Period Investment under Uncertainty," Management Science, 8, No. 2, 184-200. [2] Retrieved September 24, 2020.

[3] 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.

[4] Borch, K. H. (1968), The Economics of Uncertainty, Princeton University Press, Princeton. [4]. Retrieved September 24, 2020.

[5] 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.

[6] 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.

[7] 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.

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See also

References