Portfolio optimization based on higher order stochastic dominance: limited memory bundle algorithm approach

In economics, stochastic dominance has many applications in decision theory. Solving optimization problems with stochastic dominant constraints is challenging due to their non-smooth nature. The limited memory bundle method is an algorithm for solving large, non-smooth, and both constrained and unconstrained optimization problems. It is beneficial for problems with a large number of variables where computing the gradient is impractical. In this paper, the algorithm of the limited memory bundle method is directly applied to the portfolio optimization problem with second- and third-order stochastic dominance constraints. This new approach makes it possible to simplify high-order stochastic dominance problems to a polynomial runtime, which leads to faster performance and computational errors are significantly reduced. Numerical experiments confirm the applicability of the method based on the obtained results.