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Type  Working Paper 
Scope  Disciplinebased scholarship 
Title  A polynomial optimization approach to principalagent problems 
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Institution  University of Zurich 
Series Name  Swiss Finance Institute Research Paper 
Number  1235 
Number of Pages  39 
Date  2013 
Abstract Text  This paper presents a new method for the analysis of moral hazard principalagent problems. The new approach avoids the stringent assumptions on the distribution of outcomes made by the classical firstorder approach and instead only requires the agent's expected utility to be a rational function of the action. This assumption allows for a reformulation of the agent's utility maximization problem as an equivalent system of equations and inequalities. This reformulation in turn transforms the principal's utility maximization problem into a nonlinear program. Under the additional assumptions that the principal's expected utility is a polynomial and the agent's expected utility is rational in the wage, the final nonlinear program can be solved to global optimality. The paper also shows how to first approximate expected utility functions that are not rational by polynomials, so that the polynomial optimization approach can be applied to compute an approximate solution to nonpolynomial problems. Finally, the paper demonstrates that the polynomial optimization approach, unlike the classical approach, extends to principalagent models with multidimensional action sets. 
Official URL  http://papers.ssrn.com/sol3/papers.cfm?abstract_id=2179445 
Other Identification Number  merlinid:8776 
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