Incomplete Market Equilibria Solved on the GPU

Abstract

This paper presents a simple but effective method to exploit the Graphical Processing Unit of a PC to solve a dynamic incomplete market equilibria with heterogeneous agents. The method is an adjusted brute force search and does not use first order conditions and neither imposes differentiability nor concavity requirements on the value function. Instead, the method searches the asset allocation space and searches for the set of allocations at the Pareto Frontier. The method then picks one point on the Pareto Frontier following a Bargaining Power rule. We demonstrate the method by solving a dynamic general equilibrium economy with fixed transaction costs. Fixed transaction costs impose two difficulties: It not only amplifies market incompleteness but also induces non-differentiability in the value function which prevents one from solving the model using conventional methods. We show that our method can tackle these two difficulties by replicating main findings of the transaction costs literature. The method is massively parallel and therefore extremely suitable for Graphical Processing Unit (GPU) implementation.

Keywords: Fixed Transaction Costs, Incomplete Markets, Dynamic Portfolio Choice, GPU

JEL Classification: D52, D58, G12