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Jump-Diffusion Risk-Sensitive Asset Management II: Jump-Diffusion Factor Model

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  • Mark Davis
  • Sebastien Lleo

Abstract

In this article we extend earlier work on the jump-diffusion risk-sensitive asset management problem [SIAM J. Fin. Math. (2011) 22-54] by allowing jumps in both the factor process and the asset prices, as well as stochastic volatility and investment constraints. In this case, the HJB equation is a partial integro-differential equation (PIDE). By combining viscosity solutions with a change of notation, a policy improvement argument and classical results on parabolic PDEs we prove that the HJB PIDE admits a unique smooth solution. A verification theorem concludes the resolution of this problem.

Suggested Citation

  • Mark Davis & Sebastien Lleo, 2011. "Jump-Diffusion Risk-Sensitive Asset Management II: Jump-Diffusion Factor Model," Papers 1102.5126, arXiv.org, revised Sep 2012.
    • Handle: RePEc:arx:papers:1102.5126
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    File URL: http://arxiv.org/pdf/1102.5126
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    References listed on IDEAS

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    1. Mark H. A. Davis & Sébastien Lleo, 2014. "Risk-Sensitive Asset Management," World Scientific Book Chapters, in: RISK-SENSITIVE INVESTMENT MANAGEMENT, chapter 2, pages 17-40, World Scientific Publishing Co. Pte. Ltd..
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    Cited by:

    1. Hiroaki Hata, 2021. "Risk-Sensitive Asset Management with Lognormal Interest Rates," Asia-Pacific Financial Markets, Springer;Japanese Association of Financial Economics and Engineering, vol. 28(2), pages 169-206, June.
    2. Dariusz Zawisza, 2020. "On the parabolic equation for portfolio problems," Papers 2003.13317, arXiv.org, revised Oct 2020.
    3. Jan Obłój & Thaleia Zariphopoulou, 2021. "In memoriam: Mark H. A. Davis and his contributions to mathematical finance," Mathematical Finance, Wiley Blackwell, vol. 31(4), pages 1099-1110, October.
    4. Rudiger Frey & Verena Kock, 2021. "Deep Neural Network Algorithms for Parabolic PIDEs and Applications in Insurance Mathematics," Papers 2109.11403, arXiv.org, revised Sep 2021.

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