Chance-constrained portfolio selection

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 ${\displaystyle \sum _{j}}$wjE(Xj, subject to Pr(${\displaystyle \sum _{j}}$ wjXj < s) ≤ α, ${\displaystyle \sum _{j}}$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.