Chance-constrained portfolio selection

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This article describes the original implementation of the portfolio selection under Loss aversion. Its formulation, itself based upon the seminal work of Abraham Charnes and William W. Cooper on stochastic programming[1] assumes that investor’s preferences are representable by the expected utility of final wealth and the probability that final wealth be below a survival or safety level s. As stated by N. H. Agnew, et al [2] and Bertil Naslund and Andrew B. Whinston[3] the chance-constrained portfolio problem is: 

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.

David H. Pyle and Stephen J. Turnovsky[4] investigated the risk aversion properties of chance-constrained portfolio selection. Karl H. Borch[5] observed 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 fixed α the chance-constrained portfolio problem represents Lexicographic preferences and is an implementation of capital asset pricing under loss aversion.

Bay et al.[6] provide a survey of chance-constrained solution methods. J. Seppälä [7] compared chance-constrained solutions to mean-variance and safety-first portfolio problems.

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References[]

  1. ^ A. Chance and W. W. Cooper (1959), “Chance-Constrained Programming,” Management Science, 6, No. 1, 73-79. [1]. Retrieved September 24, 2020
  2. ^ 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. [2]. Retrieved September 24, 2020.
  3. ^ Naslund, B. and A. Whinston (1962), “A Model of Multi-Period Investment under Uncertainty,” Management Science, 8, No. 2, 184-200. [3] Retrieved September 24, 2020.
  4. ^ Pyle, D. H. and Stephen J. Turnovsky (1971), “Risk Aversion in Chance Constrained Portfolio Selection, Management Science,18, No. 3, 218-225.[4]. Retrieved September 24, 2020.
  5. ^ Borch, K. H. (1968), The Economics of Uncertainty, Princeton University Press, Princeton. [5]. Retrieved September 24, 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. ^ 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. [7]. Retrieved September 25, 2020.
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