Sample average approximation for the continuous type principal-agent problem

We develop a method for finding approximate solutions to the continuous agent type principal-agent problem when analytical methods are not available. The solution is calculated by solving a discrete agent type version of the problem using sample average approximation and bootstrapping. We show how a solution to the approximate problem can be used to derive a lower bound and expected upper bound for the optimal objective function, and evaluate the error associated with the approximation. Numerical examples illustrate convergence in the approximate solution to the true solution as the number of samples increases. This works yields a method for obtaining some tractability in continuous type principal-agent problems where solutions were previously unavailable. Published by Elsevier B.V.