Infinite-Horizon Optimal Switching Regions for a Pair-Trading Strategy with Quadratic Risk Aversion Considering Simultaneous Multiple Switchings: A Viscosity Solution Approach

Abstract

Very few studies have explored the structure of optimal switching regimes. We extend the existing research on the infinite-horizon multiple-regime switching problem with an arbitrary number of switch options by replacing the linear running reward function with a quadratic function in the objective function. To make our analysis more rigorous, we establish the theoretical basis for the application of the simultaneous multiple-regime switches to the problem with the extended objective function, and provide the sufficient condition under which each certain separated region in the space includes, at most, one single connected optimal switching region, which determines the structure of the optimal switching regions, and we identify the structure of the optimal switching regions for the particular problem.