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Minimal sufficient conditions for a primal optimizer in nonsmooth utility maximization

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Abstract

We continue the study of utility maximization in the nonsmooth setting and give a counterexample to a conjecture made in Deelstra et al. (Ann. Appl. Probab. 11:1353–1383, 2001) on the optimality of random variables valued in an appropriate subdifferential. We derive minimal sufficient conditions on a random variable for it to be a primal optimizer in the case where the utility function is not strictly concave.

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References

  1. Bouchard, B.: Utility maximization on the real line under proportional transaction costs. Finance Stoch. 6, 495–516 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  2. Bouchard, B., Touzi, N., Zeghal, A.: Dual formulation of the utility maximization problem: The case of nonsmooth utility. Ann. Appl. Probab. 14, 678–717 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  3. Deelstra, G., Pham, H., Touzi, N.: Dual formulation of the utility maximization problem under transaction costs. Ann. Appl. Probab. 11, 1353–1383 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  4. Delbaen, F., Schachermayer, W.: A general version of the fundamental theorem of asset pricing. Math. Ann. 300, 463–520 (1994)

    Article  MathSciNet  MATH  Google Scholar 

  5. Delbaen, F., Schachermayer, W.: The fundamental theorem of asset pricing for unbounded stochastic processes. Math. Ann. 312, 215–250 (1998)

    Article  MathSciNet  MATH  Google Scholar 

  6. Jacod, J., Shiryaev, A.N.: Limit Theorems for Stochastic Processes, 2nd edn. Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], vol. 288, Springer, Berlin (2003)

    MATH  Google Scholar 

  7. Karatzas, I., Žitković, G.: Optimal consumption from investment and random endowment in incomplete semimartingale markets. Ann. Probab. 31, 1821–1858 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  8. Kramkov, D., Schachermayer, W.: The asymptotic elasticity of utility functions and optimal investment in incomplete markets. Ann. Appl. Probab. 9, 904–950 (1999)

    Article  MathSciNet  MATH  Google Scholar 

  9. Protter, P.E.: Stochastic Integration and Differential Equations, 2nd edn. Applications of Mathematics (New York), vol. 21, Springer, Berlin (2004). Stochastic Modelling and Applied Probability

    MATH  Google Scholar 

  10. Rockafellar, R.T.: Convex Analysis. Princeton Mathematical, vol. 28. Princeton University Press, Princeton (1970)

    MATH  Google Scholar 

  11. Schachermayer, W.: A super-martingale property of the optimal portfolio process. Finance Stoch. 7, 433–456 (2003)

    Article  MathSciNet  MATH  Google Scholar 

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Authors and Affiliations

  1. Department of Mathematics, Humboldt Universität Berlin, Unter den Linden 6, 10099, Berlin, Germany

    Nicholas Westray

  2. Department of Mathematics, Imperial College, South Kensington, London, SW7 2AZ, UK

    Harry Zheng

Authors
  1. Nicholas Westray
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  2. Harry Zheng
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Correspondence to Harry Zheng.

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This research was funded by an EPSRC grant.

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Westray, N., Zheng, H. Minimal sufficient conditions for a primal optimizer in nonsmooth utility maximization. Finance Stoch 15, 501–512 (2011). https://doi.org/10.1007/s00780-010-0128-6

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  • DOI: https://doi.org/10.1007/s00780-010-0128-6

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