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Jump-Diffusion Risk-Sensitive Benchmarked Asset Management

In: Stochastic Programming Applications in Finance, Energy, Planning and Logistics

Author

Listed:
  • Mark Davis

    (Department of Mathematics, Imperial College London, London SW7 2AZ, England)

  • Sébastien Lleo

    (Finance Department and Value and Persuasion Research Centre, Reims Management School, 59 rue Pierre Taittinger, 51100 Reims, France)

Abstract

In earlier works (Davis and Lleo, 2011b; Davis and Lleo, 2012), we showed that jump-diffusion risk-sensitive asset management problem without benchmark admit a unique classical (C1, 2) solution. In this article we extend these solution techniques to a benchmarked asset management problem with jumps. Benchmarked asset management problems are highly relevant to the financial industry: most investment funds have a benchmark, such as a financial index or a customized portfolio, against which their performance is assessed. We show here under two different sets of assumptions that the stochastic control problem associated with the benchmarked aset management problem admits a unique C1, 2 solution and that the optimal investment strategy exists and is unique.

Suggested Citation

  • Mark Davis & Sébastien Lleo, 2013. "Jump-Diffusion Risk-Sensitive Benchmarked Asset Management," World Scientific Book Chapters, in: Horand I Gassmann & William T Ziemba (ed.), Stochastic Programming Applications in Finance, Energy, Planning and Logistics, chapter 5, pages 97-127, World Scientific Publishing Co. Pte. Ltd..
    • Handle: RePEc:wsi:wschap:9789814407519_0005
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    Cited by:

    1. 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.

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