Solving real-life portfolio problem using stochastic programming and Monte-Carlo techniques

We deal with real-life portfolio problem with Value at Risk, transaction costs and integer allocations where the random returns are modeled using the multivariate skewed t-distribution. The original problem can be formulated as a stochastic programming problem with one chance constraint which is very hard to solve exactly. It is necessary to use sampling techniques to represent the randomness by equiprobable scenarios and to solve the approximated portfolio problem by standard mixed-integer solvers. In Branda (2010), Branda and Dupacova (2008), and Ermoliev (2000), it was shown that the chance constrained problems can be reformulated using penalty functions. However, to solve the problem with penalty objectives, it is also necessary to use sampling techniques. Finally, 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 is compared.