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Jump-Diffusion Risk-Sensitive Asset Management

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  • Mark H. A. Davis
  • Sebastien Lleo

Abstract

This paper considers a portfolio optimization problem in which asset prices are represented by SDEs driven by Brownian motion and a Poisson random measure, with drifts that are functions of an auxiliary diffusion 'factor' process. 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.) By using a change of measure technique introduced by Kuroda and Nagai we show that the problem reduces to solving a certain stochastic control problem in the factor process, which has no jumps. The main result of the paper is that the Hamilton-Jacobi-Bellman equation for this problem has a classical solution. The proof uses Bellman's "policy improvement" method together with results on linear parabolic PDEs due to Ladyzhenskaya et al.

Suggested Citation

  • Mark H. A. Davis & Sebastien Lleo, 2009. "Jump-Diffusion Risk-Sensitive Asset Management," Papers 0905.4740, arXiv.org, revised Mar 2010.
    • Handle: RePEc:arx:papers:0905.4740
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    File URL: http://arxiv.org/pdf/0905.4740
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    References listed on IDEAS

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    1. Richard Bellman, 1957. "On a Dynamic Programming Approach to the Caterer Problem--I," Management Science, INFORMS, vol. 3(3), pages 270-278, April.
    2. Mark Davis & SEBastien Lleo, 2008. "Risk-sensitive benchmarked asset management," Quantitative Finance, Taylor & Francis Journals, vol. 8(4), pages 415-426.
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    Cited by:

    1. Hiroaki Hata & Jun Sekine, 2017. "Risk-Sensitive Asset Management in a Wishart-Autoregressive Factor Model with Jumps," Asia-Pacific Financial Markets, Springer;Japanese Association of Financial Economics and Engineering, vol. 24(3), pages 221-252, September.
    2. Dariusz Zawisza, 2020. "On the parabolic equation for portfolio problems," Papers 2003.13317, arXiv.org, revised Oct 2020.
    3. O. S. Rozanova & G. S. Kambarbaeva, 2015. "Optimal strategies of investment in a linear stochastic model of market," Papers 1501.07124, arXiv.org.
    4. Branger, Nicole & Kraft, Holger & Meinerding, Christoph, 2014. "Partial information about contagion risk, self-exciting processes and portfolio optimization," Journal of Economic Dynamics and Control, Elsevier, vol. 39(C), pages 18-36.
    5. Jan-Christian Gerlach & Jerome Kreuser & Didier Sornette, 2020. "Awareness of crash risk improves Kelly strategies in simulated financial time series," Papers 2004.09368, arXiv.org.
    6. Rudiger Frey & Abdelali Gabih & Ralf Wunderlich, 2013. "Portfolio Optimization under Partial Information with Expert Opinions: a Dynamic Programming Approach," Papers 1303.2513, arXiv.org, revised Feb 2014.
    7. Grzegorz Andruszkiewicz & Mark H. A. Davis & S'ebastien Lleo, 2014. "Risk-sensitive investment in a finite-factor model," Papers 1407.5278, arXiv.org, revised Jan 2016.
    8. Rüdiger Frey & Abdelali Gabih & Ralf Wunderlich, 2012. "Portfolio Optimization Under Partial Information With Expert Opinions," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 15(01), pages 1-18.

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