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**Chance constrained problems: penalty reformulation and performance of sample approximation technique.**
*(English)*
Zbl 1243.93117

Summary: 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 are solved. 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.

### MSC:

93E12 | Identification in stochastic control theory |

62D05 | Sampling theory, sample surveys |

91B30 | Risk theory, insurance (MSC2010) |

### Keywords:

chance constrained problems; penalty functions; asymptotic equivalence; sample approximation technique; investment problem### References:

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