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arxiv: 1705.07472 · v1 · submitted 2017-05-21 · 💱 q-fin.PM

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On the Black's equation for the risk tolerance function

Sigrid K\"allblad , Thaleia Zariphopoulou
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keywords functionblackequationfunctionsresultsrisktoleranceanalyze
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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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