Abstract
Consider a typical agency relation involving a capital owner and a manager. The principal (i.e., the capital owner) has a potential budget to assign to investment projects. The effective amount of investment will be a share of the potential level, given the specific form of interaction that will be established between the principal and the agent (i.e., the manager). The budget setting problem originating from this relation is evaluated from the point of view of the manager, who wants to maximize the received budget, in an intertemporal basis. The optimal control problem is subject to a constraint, which indicates how the assigned budget evolves over time. In this constraint, a matching function takes a central role; the arguments of the function are the agent’s effort to absorb new funds and the financial resources the principal has available but has not yet channeled to the manager.
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Notes
- 1.
Recall that, for any square matrix of order 2, \(Tr(J) =\lambda _{1} +\lambda _{2}\) and Det(J) = λ 1 λ 2, for λ 1 and λ 2 the eigenvalues of the matrix.
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Gomes, O. (2015). A Budget Setting Problem. In: Bourguignon, JP., Jeltsch, R., Pinto, A., Viana, M. (eds) Dynamics, Games and Science. CIM Series in Mathematical Sciences, vol 1. Springer, Cham. https://doi.org/10.1007/978-3-319-16118-1_16
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DOI: https://doi.org/10.1007/978-3-319-16118-1_16
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