## Optimal investment for executive stockholders with exponential utility

• The scope of this paper is to enhance the model for the own-company stockholder (given in Desmettre, Gould and Szimayer (2010)), who can voluntarily performance-link his personal wealth to his management success by acquiring stocks in the own-company whose value he can directly influence via spending work effort. The executive is thereby characterized by a parameter of risk aversion and the two work effectiveness parameters inverse work productivity and disutility stress. We extend the model to a constant absolute risk aversion framework using an exponential utility/disutility set-up. A closed-form solution is given for the optimal work effort an executive will apply and we derive the optimal investment strategies of the executive. Furthermore, we determine an up-front fair cash compensation applying an indifference utility rationale. Our study shows to a large extent that the results previously obtained are robust under the choice of the utility/disutility set-up.

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Author: S. Desmettre urn:nbn:de:hbz:386-kluedo-16765 Berichte des Fraunhofer-Instituts für Techno- und Wirtschaftsmathematik (ITWM Report) (196) Report English 2010 2010 Fraunhofer-Institut für Techno- und Wirtschaftsmathematik 2011/01/24 executive stockholder ; exponential utility; portfolio choice ; work effort Fraunhofer (ITWM) 5 Naturwissenschaften und Mathematik / 51 Mathematik / 510 Mathematik Standard gemäß KLUEDO-Leitlinien vor dem 27.05.2011

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