Risk management strategies via minimax portfolio optimization

Recent extreme economic developments nearing a worst-case scenario motivate further examination of minimax linear programming approaches for portfolio optimization. Risk measured as the worst-case return is employed and a portfolio from maximizing returns subject to a risk threshold is constructed. Minimax model properties are developed and parametric analysis of the risk threshold connects this model to expected value along a continuum, revealing an efficient frontier segmenting investors by risk preference. Divergence of minimax model results from expected value is quantified and a set of possible prior distributions expressing a degree of Knightian uncertainty corresponding to risk preference determined. The minimax model will maximize return with respect to one of these prior distributions providing valuable insight regarding an investor’s risk attitude and decision behavior. Linear programming models for financial firms to assist individual investors to hedge against losses by buying insurance and a model for designing variable annuities are proposed.