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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
-dimensional semimartingale, we elaborate a complete and explicit
characterization for this type of forward utilities. Furthermore, the optimal
portfolios for each of these 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. Finally,
we conclude our paper by pointing out a number of related open questions.Comment: 39 page
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