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Risk-Sensitive Control and an Optimal Investment Model

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  • W. H. Fleming
  • S. J. Sheu

Abstract

We consider an optimal investment model in which the goal is to maximize the long-term growth rate of expected utility of wealth. In the model, the mean returns of the securities are explicitly affected by the underlying economic factors. The utility function is HARA. The problem is reformulated as an infinite time horizon risk-sensitive control problem. We study the dynamic programming equation associated with this control problem and derive some consequences of the investment problem. Copyright Blackwell Publishers, Inc..

Suggested Citation

  • W. H. Fleming & S. J. Sheu, 2000. "Risk-Sensitive Control and an Optimal Investment Model," Mathematical Finance, Wiley Blackwell, vol. 10(2), pages 197-213.
  • Handle: RePEc:bla:mathfi:v:10:y:2000:i:2:p:197-213
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    References listed on IDEAS

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    1. Rheinländer, Thorsten & Schweizer, Martin, 1997. "On L2-projections on a space of stochastic integrals," SFB 373 Discussion Papers 1997,25, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
    2. David Heath & Eckhard Platen & Martin Schweizer, 2001. "A Comparison of Two Quadratic Approaches to Hedging in Incomplete Markets," Mathematical Finance, Wiley Blackwell, pages 385-413.
    3. Hans FÃllmer & Peter Leukert, 1999. "Quantile hedging," Finance and Stochastics, Springer, vol. 3(3), pages 251-273.
    4. Schweizer, Martin, 1999. "A guided tour through quadratic hedging approaches," SFB 373 Discussion Papers 1999,96, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
    5. Martin Schweizer & HuyËn Pham & (*), Thorsten RheinlÄnder, 1998. "Mean-variance hedging for continuous processes: New proofs and examples," Finance and Stochastics, Springer, vol. 2(2), pages 173-198.
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    Citations

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    Cited by:

    1. Gechun Liang & Thaleia Zariphopoulou, 2015. "Representation of homothetic forward performance processes in stochastic factor models via ergodic and infinite horizon BSDE," Papers 1511.04863, arXiv.org, revised Nov 2016.
    2. Vladimir Cherny & Jan Obloj, 2011. "Portfolio optimisation under non-linear drawdown constraints in a semimartingale financial model," Papers 1110.6289, arXiv.org, revised Apr 2013.
    3. Traian A. Pirvu & Gordan Zitkovic, 2007. "Maximizing the Growth Rate under Risk Constraints," Papers 0706.0480, arXiv.org.
    4. Vladimir Cherny & Jan Obloj, 2013. "Optimal portfolios of a long-term investor with floor or drawdown constraints," Papers 1305.6831, arXiv.org.
    5. Robertson, Scott & Xing, Hao, 2015. "Large time behavior of solutions to semi-linear equations with quadratic growth in the gradient," LSE Research Online Documents on Economics 60578, London School of Economics and Political Science, LSE Library.
    6. Jan Palczewski & Lukasz Stettner, 2007. "Growth-optimal portfolios under transaction costs," Papers 0707.3198, arXiv.org.
    7. Leitner Johannes, 2005. "Optimal portfolios with expected loss constraints and shortfall risk optimal martingale measures," Statistics & Risk Modeling, De Gruyter, pages 49-66.
    8. Tadashi Hayashi & Jun Sekine, 2011. "Risk-sensitive Portfolio Optimization with Two-factor Having a Memory Effect," Asia-Pacific Financial Markets, Springer;Japanese Association of Financial Economics and Engineering, pages 385-403.
    9. repec:eee:insuma:v:74:y:2017:i:c:p:7-19 is not listed on IDEAS
    10. Akihiko Inoue & Yumiharu Nakano, 2005. "Optimal long term investment model with memory," Papers math/0506621, arXiv.org, revised May 2006.
    11. Azzato, Jeffrey & Krawczyk, Jacek B & Sissons, Christopher, 2011. "On loss-avoiding lump-sum pension optimization with contingent targets," Working Paper Series 1532, Victoria University of Wellington, School of Economics and Finance.
    12. Tomasz R. Bielecki & Igor Cialenco & Marcin Pitera, 2013. "Dynamic Limit Growth Indices in Discrete Time," Papers 1312.1006, arXiv.org, revised Jul 2014.
    13. Thomas Knispel, 2012. "Asymptotics of robust utility maximization," Papers 1203.1191, arXiv.org.
    14. Scott Robertson & Hao Xing, 2014. "Long Term Optimal Investment in Matrix Valued Factor Models," Papers 1408.7010, arXiv.org.

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