Closed‐Form Optimal Investment Under Generalized GARCH Models

ABSTRACT This paper introduces a new class of stochastic volatility models for asset prices, the generalized Heston Nandi GARCH (GHN‐GARCH), with the primary objective of optimal dynamic asset allocation under expected utility theory for constant relative risk aversion investors. We study some of its theoretical properties, and demonstrate that the GHN‐GARCH class of models permits closed‐form solutions for optimal allocation and value function. We introduce and study in more detail an example of this class, the 4/2‐HN‐GARCH model, inspired by the continuous‐time 4/2 stochastic volatility model of Grasselli. A robust parameter estimation procedure is developed, and a numerical analysis is performed.