Chance-constrained portfolio selection

Chance-constrained portfolio selection is an approach to <a href="/facts/Portfolio_optimization/H1rvkwzX">portfolio selection</a> under <a href="/facts/Loss_aversion/R2G7bhBx">loss aversion</a>. 
The formulation assumes that (i) investor's preferences are representable by the <a href="/facts/Expected_utility/EboBlw1D">expected utility</a> of final wealth, and that (ii) they require that the probability of their final wealth falling below a <a href="/facts/Survival_analysis/q8w13cjl">survival or safety level</a> must to be acceptably low.
The chance-constrained portfolio problem is then to find:

Max 
 
 
 
 
 ∑
 
 j
 
 
 
 
 {\displaystyle \sum _{j}}
 
wjE(Xj), subject to Pr(
 
 
 
 
 ∑
 
 j
 
 
 
 
 {\displaystyle \sum _{j}}
 
 wjXj < s) ≤ α, 
 
 
 
 
 ∑
 
 j
 
 
 
 
 {\displaystyle \sum _{j}}
 
wj = 1, wj ≥ 0 for all j,
where s is the survival level and α is the admissible <a href="/facts/Ruin_theory/Jq3MaHIS">probability of ruin</a>; 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 <a href="/facts/Abraham_Charnes/3yYqsqA8">Abraham Charnes</a> and <a href="/facts/William_W._Cooper/avc9h452">William W. Cooper</a> on <a href="/facts/Chance_constrained_programming/SmRMSvFm">chance constrained programming</a> in 1959,
and was first applied to finance by <a href="/facts/Bertil_Naslund/Q1VCfFbJ">Bertil Naslund</a> and <a href="/facts/Andrew_B._Whinston/paltVvG6">Andrew B. Whinston</a> in 1962 
and in 1969 by N. H. Agnew, et al.
For fixed α the chance-constrained portfolio problem represents <a href="/facts/Lexicographic_preferences/wpy4FCh7">lexicographic preferences</a> and is an implementation of <a href="/facts/Capital_asset_pricing_model/jqUMvmlL">capital asset pricing</a> under loss aversion.
In general though, it is observed that no <a href="/facts/Utility_function/wlMDG74L">utility function</a> 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 <a href="/facts/Markowitz_model/7nYh5Gfb">mean-variance</a> and <a href="/facts/Roy%27s_safety-first_criterion/Jc2Lm997">safety-first portfolio</a> problems, see; for a survey of <a href="/facts/Numerical_solution/QT9cYa9z">solution methods</a> here, see; for a discussion of the <a href="/facts/Risk_aversion/erarEwDf">risk aversion</a> properties of chance-constrained portfolio selection, see.

Chance-constrained portfolio selection open-in-new

Chance-constrained portfolio selection