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.
In this paper, we study local stability of the mean-risk model with Conditional Value at Risk measure where the mixed-integer value function appears as a loss variable. This model has been recently introduced and studied in Schulz and Tiedemann \cite{schulz2006}. First, we generalize the qualitative results for the case with random technology matrix. We employ the contamination techniques to quantify a possible effect of changes in the underlying probability distribution on the optimal value. We use the generalized qualitative results to express the explicit formula for the directional derivative of the local optimal value function with respect to the underlying probability measure. The derivative is used to construct the bounds. Similarly, we can approximate the behavior of the local optimal value function with respect to the changes of the risk-aversion parameter which determines our aversion to risk.