J. Backhoff, F. Silva:
"Sensitivity Analysis for Expected Utility Maximization in incomplete Brownian Market Models";
Mathematics and Financial Economics, Online February 8, 2018 (2018), S. 1 - 25.

Kurzfassung englisch:
We examine the issue of sensitivity with respect to model par
ameters for the problem of utility maximization from final wealth in an incomplete Samuelson model and mainly for utility functions
of positive power-type. The method consists in moving the parameters through change of measure, which we call a weak perturbation
, decoupling the usual wealth equation from the varying para
By rewriting the maximization problem in terms of a convex-a
nalytical support function of a weakly-
compact set, crucially leveraging on the work [2], the previ
ous formulation let us prove the Hadamard directional differentiability of the value function w.r.t. the drift and interest rate parameters, as well as for volatility matrices under a stability condition on their Kernel, and derive explicit expressions for
the directional derivatives. We contrast our proposed weak
perturbations against what we call strong perturbations
, where the wealth equation is directly influenced by the chan
ging parameters. Contrary to conventional wisdom, we find that both points of view general ly yield different sensitivities unless e.g. if initial parameters and their perturbations are deterministic.

Sensitivity analysis First order sensitivity Utility maximization Weak formulation JEL Classification C02 C61

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