A bilevel optimization formulation for the setting of minimum required maintenance margins in stock exchanges

Abstract

This report addresses a hierarchical margin setting decision problem. There are two decision makers, namely, the stock exchange and the investor. The stock exchange, which is the leader in the hierarchical process, controls the margin percentage needed for each security that is traded to contain the risk of default. The leader also wants to maximize the amount of funds invested in the stock exchange. The investor, who is the follower in the hierarchical process, takes as input the margins set by the leader and chooses a portfolio that maximizes the absolute returns. A bilevel problem is proposed to model the situation and an exact solution is developed by replacing the lower level optimization problem with its Karush-Kuhn-Tucker (KKT) conditions, thereby reducing the bilevel problem into a single level problem. Four different models are considered with different complexity to determine the one apt to the real-world applications.