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On Robust Utility Maximization

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  • Traian A Pirvu
  • Ulrich G Haussmann

Abstract

This paper studies the problem of optimal investment in incomplete markets, robust with respect to stopping times. We work on a Brownian motion framework and the stopping times are adapted to the Brownian filtration. Robustness can only be achieved for logartihmic utility, otherwise a cashflow should be added to the investor s wealth. The cashflow can be decomposed into the sum of an increasing and a decreasing process. The last one can be viewed as consumption. The first one is an insurance premium the agent has to pay.

Suggested Citation

  • Traian A Pirvu & Ulrich G Haussmann, 2007. "On Robust Utility Maximization," Papers math/0702727, arXiv.org.
  • Handle: RePEc:arx:papers:math/0702727
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    References listed on IDEAS

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    6. Bruno Bouchard & Huyên Pham, 2004. "Wealth-path dependent utility maximization in incomplete markets," Finance and Stochastics, Springer, vol. 8(4), pages 579-603, November.
    7. Cox, John C. & Huang, Chi-fu, 1989. "Optimal consumption and portfolio policies when asset prices follow a diffusion process," Journal of Economic Theory, Elsevier, vol. 49(1), pages 33-83, October.
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