On the Black's equation for the risk tolerance function
Portfolio Management
2017-05-23 v1
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.
Keywords
Cite
@article{arxiv.1705.07472,
title = {On the Black's equation for the risk tolerance function},
author = {Sigrid Källblad and Thaleia Zariphopoulou},
journal= {arXiv preprint arXiv:1705.07472},
year = {2017}
}