Scalarization Methods in Multiobjective Optimization, Robustness, Risk Theory and Finance

Abstract

We show that scalarization techniques are very important tools in several fields of mathematics, especially in multiobjective optimization, uncertain optimization, risk theory and finance. Specifically, we consider randomness in scalar optimization problems and explore important connections between a nonlinear scalarization technique, robust optimization and coherent risk measures. Furthermore, we discuss a new model for a Private Equity Fund based on stochastic differential equations. In order to find efficient strategies for the fund manager we formulate a stochastic multiobjective optimization problem for a Private Equity Fund. Using a special case of the nonlinear scalarization technique, the e-constraint method, we solve this stochastic multiobjective optimization problem.