Robust portfolio choice under the 4/2 stochastic volatility model

Abstract

Abstract This paper provides the first optimal portfolio analysis for a constant relative risk-averse and ambiguity-averse investor under the state-of-the-art 4/2 stochastic volatility model in a complete market setting. We determine the robust optimal strategy and the worst case measure by allowing separate levels of uncertainty for variance and stock drivers. Technical conditions for well-defined solutions are detailed together with a verification result. The robust optimal investment exposure displays a dependence on current volatility levels similar to the non-robust case further impacted by the ambiguity-aversion level. Using real-world parameters, the numerical analysis finds that wealth-equivalent losses (WELs) from ignoring uncertainty or market completeness are moderate. On the other hand, WELs for investors who follow simpler but popular strategies, such as Heston (1/2 model) and Merton (geometric Brownian motion [GBM] model), could be quite substantial, of up to 24 and 51%, respectively. This latest analysis comes from new non-affine representations for the suboptimal value function of the 1/2 and GBM strategies.