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Risk Sensitive Investment Management with Affine Processes: A Viscosity Approach

In: Recent Advances In Financial Engineering 2009

Author

Listed:
  • Mark Davis

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

  • Sébastien Lleo

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

Abstract

In this paper, we extend the jump-diffusion model proposed by Davis and Lleo to include jumps in asset prices as well as valuation factors. The criterion, following earlier work by Bielecki, Pliska, Nagai and others, is risk-sensitive optimization (equivalent to maximizing the expected growth rate subject to a constraint on variance). In this setting, the Hamilton-Jacobi-Bellman equation is a partial integro-differential PDE. The main result of the paper is to show that the value function of the control problem is the unique viscosity solution of the Hamilton-Jacobi-Bellman equation.

Suggested Citation

  • Mark Davis & Sébastien Lleo, 2010. "Risk Sensitive Investment Management with Affine Processes: A Viscosity Approach," World Scientific Book Chapters, in: Masaaki Kijima & Chiaki Hara & Keiichi Tanaka & Yukio Muromachi (ed.), Recent Advances In Financial Engineering 2009, chapter 1, pages 1-41, World Scientific Publishing Co. Pte. Ltd..
    • Handle: RePEc:wsi:wschap:9789814304078_0001
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    Cited by:

    1. Goutte Stéphane & Ngoupeyou Armand, 2014. "Dual Optimization Problem on Defaultable Claims," Mathematical Economics Letters, De Gruyter, vol. 1(2-4), pages 1-8, July.
    2. Stephane Goutte & Armand Ngoupeyou, 2012. "Optimization problem and mean variance hedging on defaultable claims," Papers 1209.5953, arXiv.org.

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