Geodesic
Chance constrained problems: penalty reformulation and performance of sample approximation technique
Kybernetika, Tome 48 (2012) no. 1, pp. 105-122.

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We explore reformulation of nonlinear stochastic programs with several joint chance constraints by stochastic programs with suitably chosen penalty-type objectives. We show that the two problems are asymptotically equivalent. Simpler cases with one chance constraint and particular penalty functions were studied in [6,11]. The obtained problems with penalties and with a fixed set of feasible solutions are simpler to solve and analyze then the chance constrained programs. We discuss solving both problems using Monte-Carlo simulation techniques for the cases when the set of feasible solution is finite or infinite bounded. The approach is applied to a financial optimization problem with Value at Risk constraint, transaction costs and integer allocations. We compare the ability to generate a feasible solution of the original chance constrained problem using the sample approximations of the chance constraints directly or via sample approximation of the penalty function objective.
Classification : 62A10, 93E12
Keywords: chance constrained problems; penalty functions; asymptotic equivalence; sample approximation technique; investment problem 
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     author = {Branda, Martin},
     title = {Chance constrained problems: penalty reformulation and performance of sample approximation technique},
     journal = {Kybernetika},
     pages = {105--122},
     publisher = {mathdoc},
     volume = {48},
     number = {1},
     year = {2012},
     mrnumber = {2932930},
     zbl = {1243.93117},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/KYB_2012__48_1_a5/}
}
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Branda, Martin. Chance constrained problems: penalty reformulation and performance of sample approximation technique. Kybernetika, Tome 48 (2012) no. 1, pp. 105-122. http://geodesic.mathdoc.fr/item/KYB_2012__48_1_a5/