EXPLICIT DESCRIPTION OF HARA FORWARD UTILITIES AND THEIR OPTIMAL PORTFOLIOS

This paper deals with forward performances of HARA type. Precisely, for a market model in which stock price processes are modeled by a locally bounded d-dimensional semimartingale, we elaborate a complete and explicit characterization for this type of forward utilities. In particular, under some mild technical assumptions of integrability, we prove that the risk aversion process of a power-type forward utility is constant. Furthermore, the optimal portfolios for all HARA forward utilities are explicitly described. Our approach is based on the minimal Hellinger martingale densities that are obtained from the important statistical concept of Hellinger process. These martingale densities were introduced recently and appeared herein tailor-made for these forward utilities. After outlining our parametrization method for the HARA forward, we provide illustrations on discrete-time market models.