The Risk-Tolerance Process and the Sensitivity of Optimal Investment and Consumption
In the perturbation analysis of various models with small frictions, a crucial role is played by the risk tolerance of the indirect utility process. Building on work of Kramkov and Sirbu, we show that this object is well defined in a general semimartingale setting. We also establish that it admits a dynamic characterisation in terms of a quadratic BSDE, which in turn allows to compute the sensitivity of optimal investment strategies and consumption plans with respect to wealth. Together with the risk tolerance process itself, these quantities turn out to be the crucial statistics through which preferences are encoded in asymptotic analysis.
Joint work with Christoph Czichowsky and Jan Kallsen.