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Explicit Description of HARA Forward Utilities and Their Optimal Portfolios

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  • Tahir Choulli
  • Junfeng Ma

Abstract

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. 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.

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  • Tahir Choulli & Junfeng Ma, 2013. "Explicit Description of HARA Forward Utilities and Their Optimal Portfolios," Papers 1307.0785, arXiv.org.
    • Handle: RePEc:arx:papers:1307.0785
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    Cited by:

    1. Tahir Choulli & Jun Deng & Junfeng Ma, 2015. "How non-arbitrage, viability and numéraire portfolio are related," Finance and Stochastics, Springer, vol. 19(4), pages 719-741, October.

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