A chance constrained investment problem with portfolio variance and skewness criteria - solution technique based on the Successive Iterative Regularization
Abstract
We deal with an investment problem, where the variance of a portfolio is minimized and at the same time the skewness is maximized. Moreover, we impose a chance (probabilistic) constraint on the portfolio return which must be fulfilled with a high probability.
This leads to a difficult nonconvex multiobjective stochastic programming problem. Under discretely distributed returns, this problem can be solved using the CCP-SIR solver (Chance Constrained Problems: Successive Iterative Regularization) which has been recently introduced by Adam and Branda [1].
This algorithm relies on a relaxed nonlinear programming problem and its regularized version obtained by enlarging the set of feasible solutions using regularizing functions. These both formulations as well as the solution technique are discussed in details.
We report the results for a real life portfolio problem of a small investor. We compare the CCP-SIR solver with BONMIN applied to the deterministic mixed-integer reformulation.