Economics at your fingertips  

Sensitivity analysis for expected utility maximization in incomplete Brownian market models

Julio Backhoff Veraguas and Francisco Silva

Papers from

Abstract: We examine the issue of sensitivity with respect to model parameters for the problem of utility maximization from final wealth in an incomplete Samuelson model and mainly, but not exclusively, 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 parameters. By rewriting the maximization problem in terms of a convex-analytical support function of a weakly-compact set, crucially leveraging on the work of Backhoff and Fontbona (SIFIN 2016), the previous 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 changing parameters. Contrary to conventional wisdom, we find that both points of view generally yield different sensitivities unless e.g. if initial parameters and their perturbations are deterministic.

New Economics Papers: this item is included in nep-upt
Date: 2015-04, Revised 2017-02
References: View references in EconPapers View complete reference list from CitEc
Citations Track citations by RSS feed

Downloads: (external link) Latest version (application/pdf)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link:

Access Statistics for this paper

More papers in Papers from
Series data maintained by arXiv administrators ().

Page updated 2017-09-29
Handle: RePEc:arx:papers:1504.02734