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Robust utility maximization for a diffusion market model with misspecified coefficients


  • Revaz Tevzadze


  • Teimuraz Toronjadze


  • Tamaz Uzunashvili



The paper studies the robust maximization of utility from terminal wealth in a diffusion financial market model. The underlying model consists of a tradable risky asset whose price is described by a diffusion process with misspecified trend and volatility coefficients, and a non-tradable asset with a known parameter. The robust functional is defined in terms of a utility function. An explicit characterization of the solution is given via the solution of the Hamilton–Jacobi–Bellman–Isaacs (HJBI) equation. Copyright The Author(s) 2013

Suggested Citation

  • Revaz Tevzadze & Teimuraz Toronjadze & Tamaz Uzunashvili, 2013. "Robust utility maximization for a diffusion market model with misspecified coefficients," Finance and Stochastics, Springer, vol. 17(3), pages 535-563, July.
  • Handle: RePEc:spr:finsto:v:17:y:2013:i:3:p:535-563
    DOI: 10.1007/s00780-012-0199-7

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    References listed on IDEAS

    1. Ioannis Karatzas & Jaksa Cvitanic, 1999. "On dynamic measures of risk," Finance and Stochastics, Springer, vol. 3(4), pages 451-482.
    2. N. Lazrieva & T. Toronjadze, 2008. "Optimal Robust Mean-Variance Hedging in Incomplete Financial Markets," Papers 0805.0122,
    3. Hernández-Hernández Daniel & Schied Alexander, 2006. "Robust utility maximization in a stochastic factor model," Statistics & Risk Modeling, De Gruyter, vol. 24(1/2006), pages 1-17, July.
    4. Anne Gundel, 2005. "Robust utility maximization for complete and incomplete market models," Finance and Stochastics, Springer, vol. 9(2), pages 151-176, April.
    5. Hernández-Hernández, Daniel & Schied, Alexander, 2007. "A control approach to robust utility maximization with logarithmic utility and time-consistent penalties," Stochastic Processes and their Applications, Elsevier, vol. 117(8), pages 980-1000, August.
    6. Touzi, Nizar, 2000. "Direct characterization of the value of super-replication under stochastic volatility and portfolio constraints," Stochastic Processes and their Applications, Elsevier, vol. 88(2), pages 305-328, August.
    7. Denis Talay & Ziyu Zheng, 2002. "Worst case model risk management," Finance and Stochastics, Springer, vol. 6(4), pages 517-537.
    8. Tevzadze, Revaz, 2008. "Solvability of backward stochastic differential equations with quadratic growth," Stochastic Processes and their Applications, Elsevier, vol. 118(3), pages 503-515, March.
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    Cited by:

    1. repec:wsi:ijtafx:v:20:y:2017:i:07:n:s0219024917500492 is not listed on IDEAS
    2. Hu, Mingshang & Ji, Shaolin, 2017. "Dynamic programming principle for stochastic recursive optimal control problem driven by a G-Brownian motion," Stochastic Processes and their Applications, Elsevier, vol. 127(1), pages 107-134.
    3. Kim Weston, 2016. "Stability of utility maximization in nonequivalent markets," Finance and Stochastics, Springer, vol. 20(2), pages 511-541, April.
    4. Bruno Bouchard & Marcel Nutz, 2015. "Stochastic Target Games and Dynamic Programming via Regularized Viscosity Solutions," Post-Print hal-00846830, HAL.
    5. Ariel Neufeld & Mario Sikic, 2016. "Robust Utility Maximization in Discrete-Time Markets with Friction," Papers 1610.09230,, revised May 2018.
    6. Dirk Becherer & Klebert Kentia, 2017. "Good Deal Hedging and Valuation under Combined Uncertainty about Drift and Volatility," Papers 1704.02505,
    7. Ariel Neufeld & Marcel Nutz, 2015. "Robust Utility Maximization with L\'evy Processes," Papers 1502.05920,, revised Mar 2016.

    More about this item


    Maximin problem; Saddle point; Hamilton–Jacobi–Bellman–Isaacs equation; Robust utility maximization; Generalized control; 60H10; 60H30; 90C47; G3; D5;

    JEL classification:

    • G3 - Financial Economics - - Corporate Finance and Governance
    • D5 - Microeconomics - - General Equilibrium and Disequilibrium


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