Robust Worst-Case Optimal Investment

Abstract

Based on a robustness concept adapted from mathematical statistics, we investigate robust optimal investment strategies for worst-case crash scenarios when the maximum crash height is not known a priori. We specify an efficiency criterion in terms of the certainty equivalents of optimal terminal wealth and explicitly solve the investor’s portfolio problem for CRRA risk preferences. We also study the behavior of the minimax crash height and the efficiency of the associated strategies in the limiting case of infinitely many crashes.

Keywords: worst-case, crash scenario, robust optimization, Knightian uncertainty, efficiency, min-max approach

JEL Classification: G11, D81, C10