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On the Black's equation for the risk tolerance function

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  • Sigrid Kallblad
  • Thaleia Zariphopoulou

Abstract

We analyze a nonlinear equation proposed by F. Black (1968) for the optimal portfolio function in a log-normal model. We cast it in terms of the risk tolerance function and provide, for general utility functions, existence, uniqueness and regularity results, and we also examine various monotonicity, concavity/convexity and S-shape properties. Stronger results are derived for utilities whose inverse marginal belongs to a class of completely monotonic functions.

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  • Sigrid Kallblad & Thaleia Zariphopoulou, 2017. "On the Black's equation for the risk tolerance function," Papers 1705.07472, arXiv.org.
  • Handle: RePEc:arx:papers:1705.07472
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    References listed on IDEAS

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    1. Ankush Agarwal & Ronnie Sircar, 2017. "Portfolio Benchmarking under Drawdown Constraint and Stochastic Sharpe Ratio," Working Papers hal-01388399, HAL.
    2. Ankush Agarwal & Ronnie Sircar, 2016. "Portfolio Benchmarking under Drawdown Constraint and Stochastic Sharpe Ratio," Papers 1610.08558, arXiv.org.
    3. Bian, Baojun & Zheng, Harry, 2015. "Turnpike property and convergence rate for an investment model with general utility functions," Journal of Economic Dynamics and Control, Elsevier, vol. 51(C), pages 28-49.
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